-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1440458728318954895714704888643', 'a10': 2, 'a2': -1, 'a3': -1, 'a4': 1, 'a5': -2, 'a6': 1, 'a7': 0, 'a8': -1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 30.518823652533378, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 1]], [7, [1]], [13, [1, 1]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '3822.1', 'coefficient_field': '1.1.1.1', 'conductor': 3822, 'conductor_radical': 546, 'degree': 2, 'euler_factors': [[1, 1], [1, 1], [1, 2, 5], [1], [1, -3, 11], [1, 1], [1, -1, 17], [1, 3, 19], [1, 0, 23], [1, -3, 29], [1, 4, 31], [1, 2, 37], [1, -2, 41], [1, -6, 43], [1, 9, 47], [1, -1, 53], [1, -11, 59], [1, -11, 61], [1, 7, 67], [1, -15, 71], [1, 12, 73], [1, -2, 79], [1, 0, 83], [1, -10, 89], [1, 12, 97], [1, 14, 101], [1, -14, 103], [1, 4, 107], [1, 8, 109], [1, -3, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [[[1, 1], 1]], [[[1, 2, 5], 1]], [1], [[[1, -3, 11], 1]], [[[1, 1], 1]], [[[1, -1, 17], 1]], [[[1, 3, 19], 1]], [[[1, 0, 23], 1]], [[[1, -3, 29], 1]], [[[1, 4, 31], 1]], [[[1, 2, 37], 1]], [[[1, -2, 41], 1]], [[[1, -6, 43], 1]], [[[1, 9, 47], 1]], [[[1, -1, 53], 1]], [[[1, -11, 59], 1]], [[[1, -11, 61], 1]], [[[1, 7, 67], 1]], [[[1, -15, 71], 1]], [[[1, 12, 73], 1]], [[[1, -2, 79], 1]], [[[1, 0, 83], 1]], [[[1, -10, 89], 1]], [[[1, 12, 97], 1]], [[[1, 14, 101], 1]], [[[1, -14, 103], 1]], [[[1, 4, 107], 1]], [[[1, 8, 109], 1]], [[[1, -3, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 39, 'label': '2-3822-1.1-c1-0-39', '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/3822/2/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.9203836209024617e-61, 0.10060462041105483, 0.20026342434481564, 0.2979982252747781, 0.39276890774940126, 0.483449269338669, 0.5688104425841163, 0.6475135335520724, 0.7181125063236253, 0.7790677344665266, 0.8287700802422477, 0.8655748792601807, 0.8878448125882353, 0.8940003354678746, 0.8825760889156256, 0.8522815323187521, 0.8020638882506156, 0.7311713761149502, 0.6392146250167634, 0.5262240993546979, 0.3927013476256855, 0.239661902759522, 0.06866772889319966, -0.11815276739816034, -0.3180989571909297, -0.5279079824436474, -0.7437817403361092, -0.9614316836982089, -1.1761418043185887, -1.3828496497380283, -1.576244660441332, -1.7508825167967517, -1.9013135701756736, -2.0222228194506804, -2.108578303562881, -2.1557842355141497, -2.159834726101511, -2.1174635599663576, -2.0262852140716996, -1.8849221696099103, -1.6931135797812868, -1.4518005312902782, -1.1631834855624066, -0.8307480099687361, -0.4592556071020646, -0.05469731223570377, 0.3757912603735852, 0.8240536053448646, 1.2810736982248307, 1.7371727072994907, 2.182237385146698, 2.6059751877064685, 2.998189947153106, 3.3490708226802726, 3.6494863186198194, 3.8912744379668327, 4.067519573009168, 4.172806558843879, 4.203442457601799, 4.157637119025562, 4.035634383384551, 3.83978695007529, 3.5745694112212423, 3.246525712516692, 2.864149308842687, 2.4376964729910666, 1.9789355244271891, 1.500837094591009, 1.0172128522280397, 0.5423122891405374, 0.09038912521049797, -0.3247494542084678, -0.6901962450818948, -0.994384855803357, -1.2275023172857318, -1.3818581130480103, -1.4521950905615282, -1.435929110483836, -1.333306239863594, -1.1474687551407035, -0.8844241245528445, -0.5529144000088463, -0.16418695931362473, 0.2683288212015515, 0.7294307498422342, 1.2026271571433638, 1.67067948759125, 2.1161864732802753, 2.52219000096458, 2.8727812359632616, 3.153684778310978, 3.3527986638936063, 3.4606689213493937, 3.4708791562867822, 3.3803382248655116, 3.189452410550249, 2.9021725280449466, 2.5259109124522747, 2.071328147313105, 1.5519944579476033, 0.9839357466151795, 0.38507906595788155, -0.22538328965581064, -0.8276881458601499, -1.4022283967661902, -1.9302846999395156, -2.394733183583763, -2.7807006925258593, -3.0761405441154066, -3.272304372312552, -3.364089336245495, -3.3502446367823304, -3.2334267531111474, -3.0200988719371447, -2.7202763923336444, -2.347126883291418, -1.9164391694191856, -1.445982042924427, -0.9547781783990227, -0.4623229166176459, 0.012219523838027097, 0.45080831431141294, 0.8372726005566374, 1.157979678688501, 1.4023949576550283, 1.5635082144082892, 1.638106191249082, 1.6268781404411736, 1.5343482161102389, 1.3686363324058965, 1.1410569057478843, 0.8655724198142831, 0.5581256395520122, 0.235880219230921, -0.08359590016201465, -0.3831667751845578, -0.6469454628620465, -0.8610531523843199, -1.0142840399939455, -1.0986435340520502, -1.1097329685117059, -1.0469609813083194, -0.9135697745901884, -0.7164732507742623, -0.4659131021374689, -0.17494788637593037, 0.1412014943579324, 0.46591910198068515, 0.7820372376071548, 1.072714557150639, 1.3223055538229955, 1.517177703973402, 1.646434518060715, 1.7025068095427276, 1.6815805332317126, 1.583837290165591, 1.4134926944064605, 1.1786278171276725, 0.8908193760685996, 0.5645847009823958, 0.21666724690312644, -0.13480296539691056, -0.47123259501859105, -0.774525514041624, -1.0280315150474348, -1.2174338528376076, -1.3315286057079365, -1.362853653918459, -1.3081321745226415, -1.168504620486939, -0.9495337551666893, -0.6609789268653946, -0.3163478029040557, 0.06775438724332132, 0.4724470540719697, 0.8775272875009019, 1.262505534870959, 1.6076705440476262, 1.8951277656853003, 2.1097559048575962, 2.2400297705721557, 2.278663867026347, 2.2230400218143287, 2.0753933281325905, 1.8427432398159362, 1.5365701511159129, 1.1722515037173962, 0.768284650089514, 0.345335635674541, -0.07483693393221069, -0.4705262861479757, -0.8212289665539881, -1.1087410142944834, -1.3181386035994782, -1.43858846030005, -1.4639420072984854, -1.3930785283008256, -1.229976083628002, -0.9835037540510668, -0.6669442232253784, -0.2972708808459328, 0.10578232184132103, 0.5208079188761273, 0.925909077137906, 1.299914829931874, 1.6235578259999583, 1.8805473386088458, 2.0584754630649282, 2.149503258599045, 2.150785623316969, 2.064608296022696, 1.8982267611626529, 1.6634140776955681, 1.375741774055843, 1.0536339496086256, 0.7172486412892971, 0.3872514955847008, 0.08355412610701705, -0.17590727152089075, -0.3762787082882367, -0.5067119328715401, -0.5610459279714, -0.5382011905755238, -0.4422581976648549, -0.2822101093708266, -0.07139941533598908, 0.17333226316086686, 0.4327338129728935, 0.6864105567868752, 0.9141910056929974, 1.0975109317746592, 1.2207280728800975, 1.2722827742573248, 1.245627055523891, 1.139856672293979, 0.9599971247194978, 0.7169143818521254, 0.4268432437782697, 0.1105494859606533, -0.20783514338246223, -0.5022447568899201, -0.746299435389341, -0.9150209934417349, -0.9865428739305967, -0.9437095538269508, -0.7754639305295676, -0.4779304131730247, -0.05511648937123135, 0.48082435736179124, 1.109801394609227, 1.804473273775461, 2.5313908077536738, 3.252546647768312, 3.927257206508405, 4.514280423970267, 4.974056259366463, 5.270946234057928], 'positive_zeros': ['1.13632157635519827185453756303816', '2.29176214015494441446638353292596', '3.56531718909845679209008011064527', '4.18385666471602742957008584978736', '5.16094770127528571404961525433370', '6.09240079730184824533716410723797', '6.79120077635151261379087305410717', '7.39171314572294905392732190791543', '8.156194040661518321377408808114241'], 'prelabel': '2-3822-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.5243844591531985, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1027037707003348120, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.13632157635519827185453756304', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.29176214015494441446638353293', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.56531718909845679209008011065', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 30.518823652533378, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 3822, 'conductor_radical': 546, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 1, -2, 1, 0, -1, 1, 2, 3, -1, -1, 0, 2, 1, 1, -1, -3, -2, 0, -3, 0, 1, -1, 1, -1, 0, 3, -2, -4, -1, -3, -1, 0, 1, -2, 3, 1, 2, 2, 0, 6, 3, -2, 0, -9, -1, 0, 1, -1, -1, 1, 1, -6, 0, 3, -3, 11, 2, 11, 4, 0, 1, 2, 3, -7, 1, 0, 0, 15, -1, -12, 2, 1, -3, 0, -1, 2, -2, 1, -2, 0, 0, -2, -6, -3, -3, 10, 2, 0, 0, 4, 9, 6, 1, -12, 0, 3, -1], 'euler11': [1, -3, 11], 'euler13': [1, 1, 0], 'euler17': [1, -1, 17], 'euler19': [1, 3, 19], 'euler2': [1, 1, 0], 'euler23': [1, 0, 23], 'euler29': [1, -3, 29], 'euler3': [1, 1, 0], 'euler31': [1, 4, 31], 'euler37': [1, 2, 37], 'euler41': [1, -2, 41], 'euler43': [1, -6, 43], 'euler47': [1, 9, 47], 'euler5': [1, 2, 5], 'euler53': [1, -1, 53], 'euler59': [1, -11, 59], 'euler61': [1, -11, 61], 'euler67': [1, 7, 67], 'euler7': [1, 0, 0], 'euler71': [1, -15, 71], 'euler73': [1, 12, 73], 'euler79': [1, -2, 79], 'euler83': [1, 0, 83], 'euler89': [1, -10, 89], 'euler97': [1, 12, 97], 'euler_factors': [[1, 1, 0], [1, 1, 0], [1, 2, 5], [1, 0, 0], [1, -3, 11], [1, 1, 0], [1, -1, 17], [1, 3, 19], [1, 0, 23], [1, -3, 29], [1, 4, 31], [1, 2, 37], [1, -2, 41], [1, -6, 43], [1, 9, 47], [1, -1, 53], [1, -11, 59], [1, -11, 61], [1, 7, 67], [1, -15, 71], [1, 12, 73], [1, -2, 79], [1, 0, 83], [1, -10, 89], [1, 12, 97]], 'index': 39, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/3822/c', 'ModularForm/GL2/Q/holomorphic/3822/2/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/3822/2/a/c'], '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': '2-3822-1.1-c1-0-39', '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': '2-3822-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.5243844591531985, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1027037707003348120, 'z1': {'__RealLiteral__': 0, 'data': '1.13632157635519827185453756304', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20242040
{'Lhash': '1440458728318954895714704888643', 'Lhash_array': ['1440458728318954895714704888643'], 'label': '2-3822-1.1-c1-0-39', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3822/2/a/c'}
-
id: 24563165
{'Lhash': '1440458728318954895714704888643', 'Lhash_array': ['1440458728318954895714704888643'], 'label': '2-3822-1.1-c1-0-39', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3822/2/a/c/1/1'}
-
id: 36615
{'Lhash': '1027037707003348120', 'Lhash_array': ['1027037707003348120'], 'label': '2-3822-1.1-c1-0-39', 'type': 'ECQ', 'url': 'EllipticCurve/Q/3822/c'}