-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1067270834853014093301632788336', 'a10': 0, 'a2': 1, 'a3': -2, 'a4': 1, 'a5': 0, 'a6': -2, 'a7': 1, 'a8': 1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 30.742404778192963, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [5, [1]], [7, [1, -1]], [11, [1, -1]]], 'bad_primes': [2, 5, 7, 11], 'central_character': '3850.1', 'coefficient_field': '1.1.1.1', 'conductor': 3850, 'conductor_radical': 770, 'degree': 2, 'euler_factors': [[1, -1], [1, 2, 3], [1], [1, -1], [1, -1], [1, -4, 13], [1, 0, 17], [1, -4, 19], [1, 4, 23], [1, -2, 29], [1, 10, 31], [1, -6, 37], [1, 0, 41], [1, -4, 43], [1, 10, 47], [1, -14, 53], [1, -10, 59], [1, 8, 61], [1, 8, 67], [1, 4, 71], [1, 4, 73], [1, -16, 79], [1, 4, 83], [1, -10, 89], [1, 6, 97], [1, -12, 101], [1, 2, 103], [1, -12, 107], [1, 14, 109], [1, -14, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [[[1, 2, 3], 1]], [1], [[[1, -1], 1]], [[[1, -1], 1]], [[[1, -4, 13], 1]], [[[1, 0, 17], 1]], [[[1, -4, 19], 1]], [[[1, 4, 23], 1]], [[[1, -2, 29], 1]], [[[1, 10, 31], 1]], [[[1, -6, 37], 1]], [[[1, 0, 41], 1]], [[[1, -4, 43], 1]], [[[1, 10, 47], 1]], [[[1, -14, 53], 1]], [[[1, -10, 59], 1]], [[[1, 8, 61], 1]], [[[1, 8, 67], 1]], [[[1, 4, 71], 1]], [[[1, 4, 73], 1]], [[[1, -16, 79], 1]], [[[1, 4, 83], 1]], [[[1, -10, 89], 1]], [[[1, 6, 97], 1]], [[[1, -12, 101], 1]], [[[1, 2, 103], 1]], [[[1, -12, 107], 1]], [[[1, 14, 109], 1]], [[[1, -14, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 27, 'label': '2-3850-1.1-c1-0-27', 'leading_term': '2.18237423648531818644947440932000000000000000000000000000000000000000000000000000000000000', '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/3850/2/a/o', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.1823742364853183, 2.1746251982267903, 2.151315586389977, 2.11226584301895, 2.0572026175517846, 1.9857958359397216, 1.8977072006909603, 1.792647156564059, 1.6704370296878008, 1.531072973996054, 1.374788490852234, 1.2021125630697913, 1.0139208010964327, 0.8114773864204644, 0.5964659816939173, 0.37100814208968125, 0.13766810519685516, -0.10055683652048401, -0.3402608555741248, -0.577669150105746, -0.8086923534708552, -1.0289952415109083, -1.2340788071948048, -1.4193743771117948, -1.5803480404522312, -1.712613259362761, -1.8120491431884265, -1.8749215131622945, -1.898003574606504, -1.8786927669116364, -1.8151201931597531, -1.7062489556564244, -1.5519577532435294, -1.353106240811186, -1.1115789173638393, -0.8303046989535404, -0.5132498451488787, -0.16538253626621574, 0.20739186758818537, 0.5983250312268633, 0.9999485657345607, 1.4042239819474216, 1.8027170376183559, 2.18679290061349, 2.547827659260294, 2.877430902031995, 3.1676733962224994, 3.4113133517916703, 3.6020143919860734, 3.7345481923572694, 3.804974814651371, 3.8107940653305206, 3.7510617561331276, 3.626465533513341, 3.4393559633998874, 3.193729786564806, 2.895163667885651, 2.550698311089469, 2.168674452479563, 1.7585239293160408, 1.330520682532572, 0.895498137744755, 0.4645408504637849, 0.04865953986613146, -0.3415403869687579, -0.6961860527520793, -1.0064489904065668, -1.2648306806786416, -1.4654112185544101, -1.6040514643963026, -1.6785403152477034, -1.6886803784725564, -1.6363072997840888, -1.5252402315556972, -1.3611633521569944, -1.1514408783865262, -0.9048705575072309, -0.6313830840141633, -0.34169715834904696, -0.04694189182899176, 0.24174012798401762, 0.5135946458246359, 0.7586473294832111, 0.9680699990465231, 1.134506900214352, 1.2523475817866991, 1.317934675877734, 1.329697155173397, 1.2882023831314626, 1.1961233858763838, 1.0581211438975937, 0.8806451964269388, 0.67165932896362, 0.44030242636112515, 0.19649757200634277, -0.04947498348630743, -0.28742340101811914, -0.5076895281613558, -0.7015745263039576, -0.8617258390836361, -0.9824676705528177, -1.0600591476319552, -1.0928671183385477, -1.0814439918353222, -1.028505030722004, -0.9388039019058453, -0.8189098967696494, -0.6768948435599453, -0.5219421450405684, -0.36389437254935575, -0.21275923333624805, -0.07819632047470874, 0.030991298592497413, 0.10733601290451084, 0.14513102220155996, 0.14077971761228641, 0.0930495125799045, 0.0032144043567870284, -0.12492469932515098, -0.2851473884399883, -0.4690484458473335, -0.6663932127741669, -0.865580901904921, -1.0541973856709852, -1.21963388351839, -1.3497437857758787, -1.4335068233012886, -1.461668116733407, -1.4273194561772837, -1.326391545351927, -1.1580288955034719, -0.9248235002402811, -0.6328892141213232, -0.2917656750685643, 0.08585163085996365, 0.48455030164080376, 0.8867956985959907, 1.273660006394186, 1.625656866769961, 1.9236464030477274, 2.1497704948460004, 2.2883749229271992, 2.3268737125538896, 2.2565118045866055, 2.0729851260260292, 1.7768821628348077, 1.373918100965509, 0.8749412394025357, 0.2957013424895962, -0.34361954005027956, -1.0191019870062183, -1.703986904409693, -2.3697425717748675, -2.987258304590391, -3.528114396248019, -3.965872515766626, -4.27732771254251, -4.4436628512504415, -4.451448780933602, -4.293438810817748, -3.969113962776121, -3.4849457036307903, -2.8543550120052297, -2.0973601784505322, -1.2399200624800457, -0.31299396613844344, 0.6486468658428481, 1.6078085339751793, 2.5264063224154247, 3.367072693312275, 4.094769846884741, 4.678333355313594, 5.091874949675019, 5.315977594637219, 5.338624364139931, 5.155814001864887, 4.771829924493058, 4.199145177919605, 3.4579627521062877, 2.575407889893809, 1.584405744430372, 0.5222931114172694, -0.570773801406168, -1.6535432002713681, -2.6854437528642934, -3.6283302798960686, -4.448117332785193, -5.116223759841273, -5.610760076441437, -5.9174026314939985, -6.029913629414913, -5.950283292177473, -5.688488975210802, -5.261884949329149, -4.6942548614258675, -4.0145756404897615, -3.2555559424854255, -2.452023364343494, -1.6392419995346108, -0.8512450452943475, -0.1192659133547726, 0.5296543166387171, 1.0738149540310211, 1.4977043921320394, 1.7925107313772608, 1.9562738131231792, 1.993677393325344, 1.9154994453653849, 1.737756804164333, 1.4805965479947283, 1.16699976379049, 0.8213729163472759, 0.4681074013365771, 0.13018869854519696, -0.17206720046889687, -0.42208053438999193, -0.6078201698778279, -0.7223194276359849, -0.7638707711126718, -0.7358938168589773, -0.6464904154214993, -0.5077189853903764, -0.33463678113812445, -0.14417236202139413, 0.046099604413970534, 0.21920352961504214, 0.3599495335213444, 0.4559868414644209, 0.49865768564945995, 0.4835979199166764, 0.4110463601638057, 0.2858430639894625, 0.11711627300292923, -0.08232261968115767, -0.29683814639840966, -0.5090296084390398, -0.7009223084186108, -0.8552147835051946, -0.9565013326399481, -0.9923898255724459, -0.9544405079233317, -0.8388619830431406, -0.6469151699057462, -0.384993953087325, -0.06437138536746977, 0.29937854969758054, 0.6872527656853294, 1.0779344136834488, 1.4490852725685146, 1.7787362596255505, 2.0466894300730565, 2.2358424620704076, 2.3333498233317953, 2.3315434840952554, 2.2285497323445713, 2.0285565916615176, 1.7417074900586638], 'positive_zeros': ['0.841928236898133693693827923437636', '1.90180299342038294256384764449799', '3.20534751547798197471923390144344', '4.01985390884569810888213513143614', '4.81393792222345661350051442947198', '5.67159245931685041393814820696670', '5.94288495836941387185597262743087', '6.79346406485319459488796331981307', '7.53959723428449843626016510137633', '8.395542523663829789229583669980387'], 'prelabel': '2-3850-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.544583372823693, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1602634016447621260, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.841928236898133693693827923438', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.90180299342038294256384764450', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.20534751547798197471923390144', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 30.742404778192963, 'bad_primes': [2, 5, 7, 11], 'central_character': '1.1', 'conductor': 3850, 'conductor_radical': 770, 'degree': 2, 'dirichlet_coefficients': [1, 1, -2, 1, 0, -2, 1, 1, 1, 0, 1, -2, 4, 1, 0, 1, 0, 1, 4, 0, -2, 1, -4, -2, 0, 4, 4, 1, 2, 0, -10, 1, -2, 0, 0, 1, 6, 4, -8, 0, 0, -2, 4, 1, 0, -4, -10, -2, 1, 0, 0, 4, 14, 4, 0, 1, -8, 2, 10, 0, -8, -10, 1, 1, 0, -2, -8, 0, 8, 0, -4, 1, -4, 6, 0, 4, 1, -8, 16, 0, -11, 0, -4, -2, 0, 4, -4, 1, 10, 0, 4, -4, 20, -10, 0, -2, -6, 1, 1, 0], 'euler11': [1, -1, 0], 'euler13': [1, -4, 13], 'euler17': [1, 0, 17], 'euler19': [1, -4, 19], 'euler2': [1, -1, 0], 'euler23': [1, 4, 23], 'euler29': [1, -2, 29], 'euler3': [1, 2, 3], 'euler31': [1, 10, 31], 'euler37': [1, -6, 37], 'euler41': [1, 0, 41], 'euler43': [1, -4, 43], 'euler47': [1, 10, 47], 'euler5': [1, 0, 0], 'euler53': [1, -14, 53], 'euler59': [1, -10, 59], 'euler61': [1, 8, 61], 'euler67': [1, 8, 67], 'euler7': [1, -1, 0], 'euler71': [1, 4, 71], 'euler73': [1, 4, 73], 'euler79': [1, -16, 79], 'euler83': [1, 4, 83], 'euler89': [1, -10, 89], 'euler97': [1, 6, 97], 'euler_factors': [[1, -1, 0], [1, 2, 3], [1, 0, 0], [1, -1, 0], [1, -1, 0], [1, -4, 13], [1, 0, 17], [1, -4, 19], [1, 4, 23], [1, -2, 29], [1, 10, 31], [1, -6, 37], [1, 0, 41], [1, -4, 43], [1, 10, 47], [1, -14, 53], [1, -10, 59], [1, 8, 61], [1, 8, 67], [1, 4, 71], [1, 4, 73], [1, -16, 79], [1, 4, 83], [1, -10, 89], [1, 6, 97]], 'index': 27, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/3850/o', 'ModularForm/GL2/Q/holomorphic/3850/2/a/o/1/1', 'ModularForm/GL2/Q/holomorphic/3850/2/a/o'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-3850-1.1-c1-0-27', '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': '2-3850-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.544583372823693, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1602634016447621260, 'z1': {'__RealLiteral__': 0, 'data': '0.841928236898133693693827923438', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20336565
{'Lhash': '1067270834853014093301632788336', 'Lhash_array': ['1067270834853014093301632788336'], 'label': '2-3850-1.1-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3850/2/a/o'}
-
id: 24563327
{'Lhash': '1067270834853014093301632788336', 'Lhash_array': ['1067270834853014093301632788336'], 'label': '2-3850-1.1-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3850/2/a/o/1/1'}
-
id: 98528
{'Lhash': '1602634016447621260', 'Lhash_array': ['1602634016447621260'], 'label': '2-3850-1.1-c1-0-27', 'type': 'ECQ', 'url': 'EllipticCurve/Q/3850/o'}