-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '369066613078474616992568929490', 'a10': [-4.630095196313784, -1.685216833277146], 'a2': [-0.6141465171933442, 1.4237516591938257], 'a3': [0.0, 0.0], 'a4': [-0.2774095667389899, -0.29403696253816936], 'a5': [0.18476761985349718, 3.172337518923849], 'a6': [0.0, 0.0], 'a7': [0.2849603092688956, 0.06753683394880027], 'a8': [-2.3250989492603478, 0.8462668092543897], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.55', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '3262057665469282343068450537884', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.6141465171933442, -1.4237516591938257], [-1.3724832757374672, -1.4547472831460975]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.18476761985349718, -3.172337518923849], [-4.966191788709715, 0.5804645706261512]], [[1.0, 0], [-0.2849603092688956, -0.06753683394880027], [6.255428482263886, 3.141594261403235]], [[1.0, 0], [4.859262565137734, 3.1959872662065925], [4.356877426430725, 10.100377175683015]], [[1.0, 0], [0.24978378928092917, 0.029195537780871354], [12.64958331753771, 2.998006319651722]], [[1.0, 0], [3.1418927728047996, -2.636361066859069], [2.952019020337816, -16.741731801207536]], [[1.0, 0], [3.559060763644088, 2.986406574111283], [3.2993153756716764, 18.711347307231954]], [[1.0, 0], [-4.461841000461734, 1.0574757429455988], [20.55355072743848, -10.32238114461063]], [[1.0, 0], [-3.054713646769765, -4.103192514257406], [-8.317293748621617, 27.781695857149177]], [[1.0, 0], [1.6989396800680554, -5.6748537322149], [-25.90012215380103, -17.034778320194988]], [[1.0, 0], [-0.8508641810670478, -4.825490561049459], [-34.76862696907861, 12.654745303049744]], [[1.0, 0], [-0.7214903348685336, -1.6726025998743808], [-28.135907152618078, 29.822319304494997]], [[1.0, 0], [-1.9520334274239792, 0.9803480338796977], [25.677819443219803, -34.49129728846688]], [[1.0, 0], [2.196826477747622, 7.337911452968843], [-39.26792713640801, 25.826921969327884]], [[1.0, 0], [-3.525022591889744, -6.105518226981169], [-26.5, 45.89934640057525]], [[1.0, 0], [7.68464905630201, -5.054273194745875], [23.368706196310253, -54.174750305936165]], [[1.0, 0], [-2.137423987364364, 2.265537069571101], [-3.5468345635390257, -60.89679765454736]], [[1.0, 0], [4.08332902409752, -5.484862747329636], [-19.215816591643048, -64.18529732513775]], [[1.0, 0], [4.7127764356663535, 1.715310343333721], [54.38915546144744, 45.63792028774429]], [[1.0, 0], [1.7151042663981921, -0.6242469016319131], [55.921244347685395, -46.92349550711737]], [[1.0, 0], [4.28100066533609, -9.924475071741373], [-54.21308939162995, -57.46251768427085]], [[1.0, 0], [-3.999479992857228, 9.271836795176895], [-56.95805594310489, -60.37201225056304]], [[1.0, 0], [9.797234111899709, -3.565901594868966], [68.17795543758905, -57.208097262102]], [[1.0, 0], [0.3795613680829094, -6.516817014032062], [-96.34412070096847, -11.261012670147332]], [[1.0, 0], [-0.2127383075603725, 0.22548943248744485], [-5.872627719958059, -100.82912398539808]], [[1.0, 0], [-8.066744893850778, 5.30558158051568], [40.796215902033154, -94.57625900866822]], [[1.0, 0], [-5.313990080157744, 9.204100809750223], [-53.5, -92.66471820493493]], [[1.0, 0], [-8.577655619617458, -14.856935343006135], [-54.5, 94.39676901250381]], [[1.0, 0], [9.465268755227067, 4.753636635503345], [67.47892086241484, 90.63992078131994]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-3e6-81.34-c1-0-1', '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/729/2/g/b/55/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.530365582561265, 0.2901950407245486, 0.06912847450758355, -0.13556069278704624, -0.3234759681410692, -0.4908063420284505, -0.6307687452678512, -0.7346186374008407, -0.7930469753874754, -0.797803736514883, -0.743399724989512, -0.6287272364118822, -0.45841685442088487, -0.2437293091211212, -0.002783019640886864, 0.2400500646011414, 0.45568070047094245, 0.6127702281513253, 0.6810024780784906, 0.6348921695607626, 0.45772851821916005, 0.14514766278577745, -0.2922258121743075, -0.8276093896621743, -1.4188026704922292, -2.011083541974893, -2.5422403178845343, -2.949403512133561, -3.177015290457766, -3.1849894814314528, -2.9559236494294026, -2.5001755301878887, -1.8577432809138563, -1.0962037777777534, -0.30444759476873184, 0.41744642537711674, 0.9712086976174618, 1.2746730172869842, 1.275369026222479, 0.961252172114538, 0.36657445612716555, -0.4285889657099294, -1.3058187858220303, -2.122457736408955, -2.7308561054554223, -3.000269463708855, -2.838217600129699, -2.207862983941451, -1.138267656648516, 0.27474842526182225, 1.8780840101107257, 3.4804706708526614, 4.878857053425923, 5.888282474447215, 6.37057941961751, 6.257106628356459, 5.561410274061664, 4.37918600138344, 2.8749639879374596, 1.257230704777668, -0.2541722987379336, -1.4629801265470228, -2.2277289639157125, -2.483679128988306, -2.2513587565884188, -1.6300093888900657, -0.7770047277224191, 0.12299180525450067, 0.8933072069351188, 1.398176899700333, 1.5668553928584532, 1.4041478379106265, 0.9852940683406511, 0.4363474332929678, -0.09575006421236758, -0.47694808061514715, -0.6163596794077015, -0.4863284866647179, -0.12776165340905982, 0.3605607982995923, 0.8463639335705226, 1.1964059006536114, 1.3095958525388565, 1.1428152614193194, 0.7230744241596234, 0.14272053532349058, -0.46160017951661375, -0.9415514413245639, -1.173614591236062, -1.0905765223494186, -0.6999770905259896, -0.08442399981661085, 0.6169781537232788, 1.2420975707785396, 1.6461832008591004, 1.739091351286402, 1.5095204198560264, 1.0292897729170853, 0.43551028174933354, -0.10584195517402788, -0.44632593054160014, -0.4995872151193508, -0.2719078202181681, 0.13057377951541102, 0.521833439725718, 0.6801065852051438, 0.4065897655811156, -0.41551147823813617, -1.7770440520044175, -3.5268696715759305, -5.390356572875917, -7.020711806302352, -8.072988765847635, -8.284137898240736, -7.539803284190485, -5.910627472376263, -3.6473719123967885, -1.1337786141943282, 1.193496303869897, 2.9399706259701595, 3.8410737332620473, 3.8211407681638296, 3.008680717974106, 1.703357878732214, 0.3020363526834468, -0.7983765331908309, -1.2974182688126195, -1.0628525638568964, -0.15970687482001228, 1.1707149169016442, 2.5763250014920462, 3.687209895439964, 4.2118419458962375, 4.011477586208607, 3.1334566002683863, 1.7950628208481751, 0.3228221113750082, -0.9359629143935799, -1.7052693156362067, -1.851056649775052, -1.4117454872693083, -0.5808652420752946, 0.35240557798054606, 1.0874230298435765, 1.396901542315089, 1.1884578134433033, 0.5259327754982271, -0.3946703765441488, -1.3066266825257944, -1.952584300230595, -2.159455264046341, -1.8861945997022282, -1.2309986124471872, -0.39683715389097624, 0.37317837383124397, 0.8701239410170583, 0.9802184043434328, 0.7138974008289505, 0.194812842929928, -0.3865880306175698, -0.8389273828536338, -1.033057726659469, -0.9413947884397359, -0.6402849732316683, -0.27473345928568, 0.0022483538129845445, 0.09429269121566661, 0.00679030835855243, -0.1452501523041805, -0.1721533555293715, 0.12184380069710571, 0.8580632600489835, 2.0185187911868088, 3.4213169478477137, 4.749425510804602, 5.629165258096874, 5.737974434065968, 4.909628130092653, 3.203224654463193, 0.9110943675325903, -1.5018308073291369, -3.5137731806965276, -4.685652975805946, -4.783957521188439, -3.849489055859334, -2.1893462318734485, -0.2919725447352882, 1.3114654079744983, 2.1990334765073545, 2.177851711042655, 1.3351422402365927, 0.004319889777298579, -1.3440606396400052, -2.2531830655109033, -2.4258213034887866, -1.81926346024474, -0.6588640889553986, 0.6348570548819332, 1.5832549889386727, 1.8076852858858508, 1.1583217006054614, -0.22810053239102193, -1.961295991804271, -3.5122113576563674, -4.374456000099139, -4.222057619315525, -3.0139437193381045, -1.0120918420385925, 1.2925714934219266, 3.323399468136494, 4.585651450287241, 4.806566264671967, 4.005356661305831, 2.4734929967171952, 0.6744330349903634, -0.9028159419295436, -1.8884371343203086, -2.129451353191723, -1.7121256963663893, -0.9069215978304568, -0.05943246939937478, 0.5324927336474953, 0.7128770263370604, 0.5028282598673879, 0.06907196095036933, -0.3577402137388559, -0.581130085855805, -0.5150706768253721, -0.21007364070049467, 0.17903292678067317, 0.46879659988207084, 0.534451373020269, 0.3723804375990242, 0.11087651205658634, -0.03733707062133646, 0.13602352440823037, 0.738877369252375, 1.7147818894037548, 2.8394044375838288, 3.7838994073779615, 4.225866691395655, 3.9688568684154535, 3.0255451955268993, 1.630623005482281, 0.17384832218118765, -0.9269697594740155, -1.369781660725333, -1.0770578076140567, -0.22793230645284476, 0.8016257183453815, 1.5728045112534932, 1.7461464972795524, 1.2134945724049104, 0.14970989398813458, -1.0385660678617166, -1.8530247246538556, -1.8853567016312605], 'positive_zeros': ['0.29114222247993840085395185283715', '1.75141170109731583074583278245598', '2.67030142742912474995534052430241', '4.30027305278469060169953453650682', '5.06053120070828127486365018104854', '6.10239348818040969834613464248432', '7.47755922543310945449371664131895', '8.357349852249861939383437772906567', '9.225603447029378571376817645198185', '9.784680957866208854179113160537414'], 'prelabel': '2-3e6-81.34-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.6546123992495355, 'root_number': '-0.4668533206382401 + 0.8843347652382827*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.327306199625', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.29114222247993840085395185284', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.75141170109731583074583278246', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.67030142742912474995534052430', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '81.34', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/g/b/55/2'], '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': '2-3e6-81.34-c1-0-1', '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': '2-3e6-81.34-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.32730619962476776, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.29114222247993840085395185284', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '369066613078474616992568929490', 'Lhash_array': ['369066613078474616992568929490'], 'label': '2-3e6-81.34-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/g/b/55/2'}