-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1965408640501324065709150400766', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': -1, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 44.46070384544894, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [29, [1, 1]]], 'bad_primes': [2, 3, 29], 'central_character': '5568.1', 'coefficient_field': '1.1.1.1', 'conductor': 5568, 'conductor_radical': 174, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, -1, 5], [1, 1, 7], [1, 2, 11], [1, 0, 13], [1, 3, 17], [1, 1, 19], [1, -4, 23], [1, 1], [1, 4, 31], [1, 3, 37], [1, 7, 41], [1, -9, 43], [1, -1, 47], [1, -2, 53], [1, 3, 59], [1, 6, 61], [1, -12, 67], [1, 16, 71], [1, 10, 73], [1, 10, 79], [1, 0, 83], [1, -6, 89], [1, 0, 97], [1, 18, 101], [1, -1, 103], [1, -17, 107], [1, -16, 109], [1, 5, 113]], 'euler_factors_factorization': [[1], [[[1, -1], 1]], [[[1, -1, 5], 1]], [[[1, 1, 7], 1]], [[[1, 2, 11], 1]], [[[1, 0, 13], 1]], [[[1, 3, 17], 1]], [[[1, 1, 19], 1]], [[[1, -4, 23], 1]], [[[1, 1], 1]], [[[1, 4, 31], 1]], [[[1, 3, 37], 1]], [[[1, 7, 41], 1]], [[[1, -9, 43], 1]], [[[1, -1, 47], 1]], [[[1, -2, 53], 1]], [[[1, 3, 59], 1]], [[[1, 6, 61], 1]], [[[1, -12, 67], 1]], [[[1, 16, 71], 1]], [[[1, 10, 73], 1]], [[[1, 10, 79], 1]], [[[1, 0, 83], 1]], [[[1, -6, 89], 1]], [[[1, 0, 97], 1]], [[[1, 18, 101], 1]], [[[1, -1, 103], 1]], [[[1, -17, 107], 1]], [[[1, -16, 109], 1]], [[[1, 5, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 102, 'label': '2-5568-1.1-c1-0-102', '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/5568/2/a/bc', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-1.0215711603598222e-60, 0.22148330129097163, 0.44213447128077066, 0.6610784213341966, 0.8773569859324958, 1.089894276413756, 1.2974697653614962, 1.4987008519410883, 1.6920360801309886, 1.8757595894566346, 2.0480068193406904, 2.206790996418889, 2.3500395257802533, 2.475639084616487, 2.581487972805527, 2.665554096858513, 2.7259368376455537, 2.760930966404139, 2.7690907191712593, 2.7492921123323644, 2.700791580421458, 2.6232790434367543, 2.5169235684025306, 2.382409883218562, 2.2209641344803814, 2.0343674586603413, 1.8249561602250528, 1.5956075616120786, 1.3497109071762332, 1.091123062766009, 0.8241091488242651, 0.5532686699930649, 0.2834481482933223, 0.019641718400106836, -0.23311841080734544, -0.4698792986700301, -0.6858896989232105, -0.8767245092677347, -1.0384079091663012, -1.167531655300186, -1.261364900868229, -1.317951904530604, -1.3361941055142896, -1.3159132684092252, -1.2578927462489355, -1.1638943715450352, -1.0366490559497552, -0.8798198499131641, -0.6979369696989765, -0.49630512206636146, -0.2808843248028151, -0.058146308916984336, 0.16509053206374372, 0.3818438381070357, 0.5851630421629511, 0.7683329351877177, 0.9250792299024215, 1.049769921635374, 1.1376060271287647, 1.184795260984046, 1.1887023978787556, 1.1479704738683205, 1.0626076020042585, 0.9340350086322691, 0.7650929217658682, 0.5600021387711922, 0.32428043667529255, 0.06461442726936192, -0.21131104262696412, -0.49502233610945234, -0.7775002380278858, -1.0494504806882763, -1.3015939029167427, -1.5249675329911605, -1.7112271026124275, -1.8529410025545634, -1.9438655141260595, -1.979191317689858, -1.9557518027385357, -1.8721845837047462, -1.7290388491544044, -1.5288227133676935, -1.2759865596154367, -0.9768404123892359, -0.6394055890092252, -0.2732031875544898, 0.11101571117072664, 0.5015909986846876, 0.8863164257682583, 1.2528333392168947, 1.589042648060161, 1.8835212508786416, 2.1259284585092626, 2.307387746236132, 2.4208294964716215, 2.4612812583943207, 2.4260934465903388, 2.315090297438537, 2.130638250313369, 1.8776266516129227, 1.5633587062835193, 1.1973538217283053, 0.7910657885359017, 0.3575244989930802, -0.08908800820355268, -0.5339135952084568, -0.9619302019301335, -1.3584823304515983, -1.7098107676924144, -2.0035619142268266, -2.229257256406889, -2.378704440958263, -2.4463330777931858, -2.4294407698100215, -2.3283378801914933, -2.146383102312279, -1.8899058735390926, -1.5680159291286535, -1.1923046666735118, -0.7764473149219686, -0.33571899889189727, 0.11355850563415434, 0.554619392600072, 0.9708834462860509, 1.3465886722806586, 1.6674022499741847, 1.9209853914133526, 2.097488956599801, 2.1899589105509496, 2.194633850165331, 2.111120776840808, 1.9424399046620713, 1.6949344022340653, 1.3780463711010296, 1.003965848632912, 0.5871649615966056, 0.14383432084232203, -0.3087568810116285, -0.7529520283958543, -1.1714218441190645, -1.5478735870135392, -1.8677252017348323, -2.1187158571578166, -2.2914264612073545, -2.3796870609517233, -2.3808524137507905, -2.295932285497562, -2.1295689893953145, -1.8898610814680659, -1.588038709227, -1.2380025847316058, -0.8557446369335809, -0.4586738146730808, -0.06487500737195827, 0.307667593940343, 0.6418493312161073, 0.9221921380844507, 1.1355267361866754, 1.2715792531676349, 1.3234353280849216, 1.2878598232483223, 1.1654563854845787, 0.9606580402695499, 0.6815474615257309, 0.33951320981286554, -0.051244272669005796, -0.4743361261959137, -0.9119110478983307, -1.345451793701285, -1.7566065768300707, -2.1280176652057956, -2.444109121865212, -2.691797032810656, -2.8610886942053884, -2.9455419725892744, -2.9425622163379557, -2.8535214211019, -2.6836925129608455, -2.442000240273866, -2.140598858203826, -1.7942951363104478, -1.4198428147279214, -1.0351411008113358, -0.6583748043754741, -0.3071369875706474, 0.002423635468201106, 0.2563889755367753, 0.44375263611298105, 0.5569615080922748, 0.5922899947121525, 0.550026804058469, 0.4344631920293637, 0.25368117743407653, 0.019150122008242447, -0.25485031079676773, -0.551953913656328, -0.8545437993141026, -1.1446596443984525, -1.404931396578171, -1.6194925100654083, -1.7748260713099668, -1.8604998196748626, -1.869750970951533, -1.799888713553274, -1.652490959096495, -1.4333819870424027, -1.1523885466914447, -0.8228832344950283, -0.46113498736993125, -0.08549675991682212, 0.28453065038049663, 0.629312580433007, 0.9301213551147662, 1.1701507175008659, 1.335450839189836, 1.4157339341159394, 1.4050061387887691, 1.3019893474760345, 1.1103067417430716, 0.8384173576208764, 0.4992976282240765, 0.10988079957335015, -0.30972221488965035, -0.7371852567725805, -1.1490671898533202, -1.5219965565846882, -1.8338817273106607, -2.065085118508965, -2.1995006330963762, -2.22547718917105, -2.136537924860633, -1.9318541092158301, -1.6164445185933722, -1.2010844936846203, -0.7019234125267857, -0.13982416945307646, 0.46054732261664744, 1.0718413429110616, 1.665299664787475, 2.2121254788665348, 2.684880631130742, 3.0588404002127785, 3.3132371198258332, 3.4323285876688847, 3.4062352075376636, 3.231500823414637, 2.9113456957991954, 2.4555953753652227, 1.8802855749723504, 1.2069596888325527, 0.4616914942950825, -0.32612004391372296, -1.1251248393501727, -1.9034964255449187, -2.6304334737370128, -3.2776122825969276, -3.8205164782130088], 'positive_zeros': ['1.55043403927507266818260846832970', '2.40278571255931783907696061947668', '3.15180062711171312966538958083021', '4.01784904516228166533670514382900', '4.86568488345684431399643303344137', '5.66001517853972341170053534434758', '6.38991396091088670282194998293756', '7.17978945507135438771144773415099', '7.72848349557465175499031616471409'], 'prelabel': '2-5568-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.667886010232099, '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': 177236637132189632, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.55043403927507266818260846833', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.40278571255931783907696061948', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.15180062711171312966538958083', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 44.46070384544894, 'bad_primes': [2, 3, 29], 'central_character': '1.1', 'conductor': 5568, 'conductor_radical': 174, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 1, 0, -1, 0, 1, 0, -2, 0, 0, 0, 1, 0, -3, 0, -1, 0, -1, 0, 4, 0, -4, 0, 1, 0, -1, 0, -4, 0, -2, 0, -1, 0, -3, 0, 0, 0, -7, 0, 9, 0, 1, 0, 1, 0, -6, 0, -3, 0, 2, 0, -2, 0, -1, 0, -3, 0, -6, 0, -1, 0, 0, 0, 12, 0, 4, 0, -16, 0, -10, 0, -4, 0, 2, 0, -10, 0, 1, 0, 0, 0, -3, 0, -1, 0, 6, 0, 0, 0, -4, 0, -1, 0, 0, 0, -2, 0], 'euler11': [1, 2, 11], 'euler13': [1, 0, 13], 'euler17': [1, 3, 17], 'euler19': [1, 1, 19], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, 1, 0], 'euler3': [1, -1, 0], 'euler31': [1, 4, 31], 'euler37': [1, 3, 37], 'euler41': [1, 7, 41], 'euler43': [1, -9, 43], 'euler47': [1, -1, 47], 'euler5': [1, -1, 5], 'euler53': [1, -2, 53], 'euler59': [1, 3, 59], 'euler61': [1, 6, 61], 'euler67': [1, -12, 67], 'euler7': [1, 1, 7], 'euler71': [1, 16, 71], 'euler73': [1, 10, 73], 'euler79': [1, 10, 79], 'euler83': [1, 0, 83], 'euler89': [1, -6, 89], 'euler97': [1, 0, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, -1, 5], [1, 1, 7], [1, 2, 11], [1, 0, 13], [1, 3, 17], [1, 1, 19], [1, -4, 23], [1, 1, 0], [1, 4, 31], [1, 3, 37], [1, 7, 41], [1, -9, 43], [1, -1, 47], [1, -2, 53], [1, 3, 59], [1, 6, 61], [1, -12, 67], [1, 16, 71], [1, 10, 73], [1, 10, 79], [1, 0, 83], [1, -6, 89], [1, 0, 97]], 'index': 102, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/5568/bc', 'ModularForm/GL2/Q/holomorphic/5568/2/a/bc/1/1', 'ModularForm/GL2/Q/holomorphic/5568/2/a/bc'], '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': '2-5568-1.1-c1-0-102', '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': '2-5568-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.667886010232099, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 177236637132189632, 'z1': {'__RealLiteral__': 0, 'data': '1.55043403927507266818260846833', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 21327380
{'Lhash': '1965408640501324065709150400766', 'Lhash_array': ['1965408640501324065709150400766'], 'label': '2-5568-1.1-c1-0-102', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5568/2/a/bc'}
-
id: 24570925
{'Lhash': '1965408640501324065709150400766', 'Lhash_array': ['1965408640501324065709150400766'], 'label': '2-5568-1.1-c1-0-102', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5568/2/a/bc/1/1'}
-
id: 27171
{'Lhash': '177236637132189632', 'Lhash_array': ['177236637132189632'], 'label': '2-5568-1.1-c1-0-102', 'type': 'ECQ', 'url': 'EllipticCurve/Q/5568/bc'}