-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3929262330964962699815781020283', 'a10': [-3.94576252741237, -1.9166834870751412], 'a2': [1.9319667999887817, 0.3406578726710167], 'a3': [0.12065648800681827, -0.14379280305192588], 'a4': [1.7370626884743336, 0.6322391136590825], 'a5': [-2.1504279521788265, -0.6129107785705672], 'a6': [0.28208847942548904, -0.23670033904528762], 'a7': [0.5863576050137126, -0.33853372109605123], 'a8': [-0.25731597008057305, -0.14856144459280854], 'a9': [0.5148261508894005, 2.9197241898028214], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.758578819202164, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [2.1504279521788265, 0.6129107785705672]]], [19, [[1.0, 0], [-3.008241715730875, 3.1544384254153006]]]], 'bad_primes': [5, 19], 'central_character': '95.74', 'coefficient_field': 'CDF', 'conductor': 95, 'conductor_radical': 95, 'conjugate': '3896075148950131084766585594898', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.9319667999887817, -0.3406578726710167], [1.8793852415718169, 0.6840402866513374]], [[1.0, 0], [-0.12065648800681827, 0.14379280305192588], [-0.520944533000791, -2.9544232590366244]], [[1.0, 0], [2.1504279521788265, 0.6129107785705672]], [[1.0, 0], [-0.5863576050137126, 0.33853372109605123], [3.5, -6.06217782649107]], [[1.0, 0], [1.4203451197913697, -2.4601099117611556], [-5.5, -9.526279441628825]], [[1.0, 0], [3.0639305602154017, 3.651450252595895], [-2.2574263096700946, 12.802500789158705]], [[1.0, 0], [-5.105181418969479, -0.9001812255758451], [15.974774553360442, 5.814342436536369]], [[1.0, 0], [-3.008241715730875, 3.1544384254153006]], [[1.0, 0], [0.35943402379648776, -0.9875368641645654], [-17.619022191736494, -14.784115022790404]], [[1.0, 0], [-0.24763015778731048, -1.4043804118482386], [-27.251086002791343, 9.918584156444393]], [[1.0, 0], [0.13553181872134326, 0.23474799606758126], [-15.5, 26.846787517317598]], [[1.0, 0], [0, -0.6037544281957674], [-37.0, 0]], [[1.0, 0], [-5.159795229889458, -4.329582274350533], [7.119575284344144, 40.37711787350053]], [[1.0, 0], [1.9253822778218543, 5.289944332133651], [-32.93991105411605, 27.639867216521193]], [[1.0, 0], [7.775427302971564, -1.3710176200511388], [44.16555317693769, -16.07494673630643]], [[1.0, 0], [2.3559354053229717, -6.4728793278185375], [-40.60035548530583, -34.067743313386586]], [[1.0, 0], [-1.7577850985683767, 9.968894672305758], [-55.44186462636859, -20.179188456214455]], [[1.0, 0], [-7.021339094126684, -2.555558434951734], [46.728711030257664, 39.2100441908789]], [[1.0, 0], [4.054781378031459, -0.714967357821196], [62.95940559265586, -22.915349602819806]], [[1.0, 0], [-7.146799262248624, 2.601222201734154], [54.38915546144744, -45.63792028774429]], [[1.0, 0], [-10.36647851291817, 12.354288010320913], [-12.676316969685915, -71.89096596989118]], [[1.0, 0], [11.373280284432786, 9.543315291943381], [13.718206035687498, 77.79981248796443]], [[1.0, 0], [12.281548561165854, -7.090755367854566], [41.5, -71.88010851410841]], [[1.0, 0], [6.3105854075848695, -5.295209888017189], [15.4546878123568, -87.64789001808651]], [[1.0, 0], [5.641438626996206, 0.9947378399503491], [91.15018421623311, 33.17595390258987]], [[1.0, 0], [1.5491827740375856, -1.2999186943211338], [17.538465944359967, -99.46558305423301]], [[1.0, 0], [15.79270234599162, 9.117920950689896], [51.5, 89.20061658979718]], [[1.0, 0], [-5.380973673721875, 3.106706599025614], [53.5, -92.66471820493493]], [[1.0, 0], [-15.024292364908078, 5.468395211739509], [83.49884429996861, -70.06384945583278]], [[1.0, 0], [0, -7.883919892208268], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-95-95.74-c1-0-5', '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/95/2/p/a/74/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.6295002037732915, 1.635495612877596, 1.6641908967438122, 1.7130937065590808, 1.7785695960444567, 1.8561831625377823, 1.9409884504097006, 2.02773231555672, 2.110986834098229, 2.185248964074855, 2.245043916496984, 2.2850567466719407, 2.3003036508158745, 2.2863437608613615, 2.2395241703551387, 2.157244842230135, 2.0382253465796953, 1.882751785766146, 1.6928798219314907, 1.4725686618901614, 1.227721498371876, 0.9661105724524989, 0.6971699465341905, 0.431646351476488, 0.18110798773064127, -0.042677427153597514, -0.22847136865417844, -0.36636284551925613, -0.44858677591344565, -0.4703022669093082, -0.43026339963803323, -0.33131243912678743, -0.18062841936874235, 0.010326393241530745, 0.2262032506271593, 0.44852499924091815, 0.6567950086615721, 0.8299140019682828, 0.9478278809473708, 0.9932972079730228, 0.953651494284835, 0.822372355056476, 0.6003421930048838, 0.2966020114399147, -0.07151512801604176, -0.47896932066026754, -0.8943579510522216, -1.2819931106325129, -1.6046138142537916, -1.8265610068095628, -1.9171765198886341, -1.8541347777564627, -1.6263855831191543, -1.236383934157299, -0.7013126450703266, -0.05306681920677837, 0.6631362002704214, 1.3915377291481013, 2.069889668742528, 2.6345177558638273, 3.0260071999959806, 3.1950182468437522, 3.107675500867557, 2.7499623891638123, 2.130598071214264, 1.2819798280638353, 0.2589343873216858, -0.8647751028580839, -2.002011672960168, -3.05949185413827, -3.9460662304896545, -4.581283881660077, -4.903384595324615, -4.875863204930817, -4.491845668382596, -3.7757036193013933, -2.781599016346078, -1.5889685866931527, -0.2952958943949449, 0.9931612695822003, 2.171758148413514, 3.1478654845868217, 3.8501379225669505, 4.235582740697225, 4.293578662105026, 4.0463230604051255, 3.5455934925803887, 2.86614954949864, 2.0965196047126105, 1.3282595225124978, 0.6449885964838141, 0.1125671766294332, -0.228335091288058, -0.36631491598648575, -0.31941074206592596, -0.13134240170129594, 0.13568984839039158, 0.41067154195415073, 0.6245693559831964, 0.7207343142781327, 0.6634160680074893, 0.4431314781503826, 0.078061060274978, -0.388786834626884, -0.8962793109392635, -1.3747716858396168, -1.7572007226414896, -1.9899576682682443, -2.041819117927456, -1.9094584082421786, -1.6185463891196477, -1.2201146458797039, -0.7826016284190137, -0.380719102182662, -0.08284725831823904, 0.0610077607555005, 0.02864670531710861, -0.16922763540145352, -0.48936082690696747, -0.8620113979246846, -1.202063123038447, -1.423633687489876, -1.4559420934306972, -1.2578345911006534, -0.8284109124319176, -0.21165911429784073, 0.506149876926309, 1.2064511237115971, 1.7546961782378905, 2.020810630499222, 1.9007918221859095, 1.3360427580240677, 0.3271693605112194, -1.060360493678598, -2.7001624451722295, -4.418509941562106, -6.016030210413061, -7.294638606274833, -8.085840260936346, -8.27611065547849, -7.825317549404811, -6.775057996568517, -5.245238610987265, -3.419011754365989, -1.5180170728829405, 0.22853217555445254, 1.6163059953686592, 2.494885947818044, 2.788829666585561, 2.507422180990632, 1.7415245231304926, 0.6479860543285996, -0.5758980424757095, -1.7237685570289645, -2.6123387228352373, -3.109073788917111, -3.15095297922867, -2.751365771077692, -1.9942172060886139, -1.01650359179475, 0.01741115868544809, 0.9451865934855437, 1.6343511941622018, 2.003738256865297, 2.0348694207803906, 1.771518575434958, 1.3078774555876458, 0.7678424358886512, 0.2795583584039045, -0.04981595316209416, -0.15427465221206746, -0.020266166257598438, 0.31289025803874726, 0.7633232431049816, 1.2253779866467756, 1.5928691660252552, 1.7819654225345836, 1.748946039799811, 1.4991367026936884, 1.0851669659192307, 0.5949331062776237, 0.13184109932308863, -0.20841064959360656, -0.35943420067206655, -0.29931441241408985, -0.05579410003757625, 0.2999647758904162, 0.670017963759427, 0.9533055997282052, 1.0712743536374025, 0.989702465826095, 0.7315155191286545, 0.37708065379286915, 0.05101840454223016, -0.10252860259595518, 0.048416455825803444, 0.5914236383114363, 1.5438213609829248, 2.8393345594998207, 4.3310320987415345, 5.811246994391494, 7.0456333149873815, 7.815411620198191, 7.959800139154355, 7.410113840567625, 6.208223112012484, 4.5048331560316415, 2.5368781107031637, 0.5874810175260967, -1.064426861795063, -2.1953744729237807, -2.679512569901292, -2.5131307162645893, -1.816222559835609, -0.8101983877678608, 0.22443549396281323, 1.0025297866353207, 1.2903858841278368, 0.9524655367077394, -0.02062509373975237, -1.5086156257417989, -3.2834320844054172, -5.052280120405092, -6.513506169012163, -7.414185369299393, -7.598015406910192, -7.034059329116561, -5.820786584388386, -4.164906653105109, -2.339623447511203, -0.6310853107610694, 0.7159064711807265, 1.5419160529400728, 1.7979665846939543, 1.5472145979950773, 0.9437551529687375, 0.1939404967693112, -0.49083189498807894, -0.9393590014985882, -1.05418965031859, -0.826712922857505, -0.33135856865138213, 0.2987053098671108, 0.9078516540866672, 1.357189984186264, 1.557251879582949, 1.4866021065717339, 1.192434862350511, 0.7737201520553401, 0.3517638682581271, 0.03609692057703035, -0.1053279369699243, -0.0638405730827474, 0.10897877025140094, 0.31735953026883446, 0.45025526848762815, 0.4154797452597057], 'positive_zeros': ['3.09964143925584336037078368913413', '4.11872259833425170054916535550667', '5.47700292752309601749973606820767', '6.88456725951318445857883444574647', '8.279471638115567049935578807608486', '9.778231556799493172995306541994008', '11.40895284134723795795985915290267', '11.93904465079112556821611542725899', '12.77248741244904539581482978266750', '14.30382948198138804080346518446248'], 'prelabel': '2-95-95.74-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8709643042066443, 'root_angle': -0.05302702141188152, 'root_number': '0.9861560632915991 - 0.16581983847904233*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0265135107059', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.09964143925584336037078368913', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.11872259833425170054916535551', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.47700292752309601749973606821', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.758578819202164, 'bad_primes': [5, 19], 'central_character': '95.74', 'conductor': 95, 'conductor_radical': 95, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/95/2/p/a/74/8'], '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': '2-95-95.74-c1-0-5', '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': '2-95-95.74-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8709643042066443, 'root_angle': -0.02651351070594076, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.09964143925584336037078368913', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3929262330964962699815781020283', 'Lhash_array': ['3929262330964962699815781020283'], 'label': '2-95-95.74-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/95/2/p/a/74/8'}