-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '963653697578028872713578444383', 'a10': [0.0, 0.0], 'a2': [-171.423322050531, 0.0], 'a3': [-729.0, 0.0], 'a4': [21193.95534284007, 0.0], 'a5': [0.0, 0.0], 'a6': [124967.60177483711, 0.0], 'a7': [162071.87964271058, 0.0], 'a8': [-2228838.3780222954, 0.0], 'a9': [531441.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 80.42319671393456, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '6.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [729.0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '75.1', 'coefficient_field': 'CDF', 'conductor': 75, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[[1.0, 0], [171.423322050531, 0], [8192.0, 0]], [[1.0, 0], [729.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-162071.87964271058, 0], [96889010407.0, 0]], [[1.0, 0], [-6405307.353520083, 0], [34522712143931.0, 0]], [[1.0, 0], [20224760.65941564, 0], [302875106592253.0, 0]], [[1.0, 0], [-134243291.6164917, 0], [9904578032905936.0, 0]], [[1.0, 0], [-195769845.7831681, 0], [42052983462257060, 0]], [[1.0, 0], [-1345735947.8564708, 0], [504036361936467400, 0]], [[1.0, 0], [-4259766178.7640076, 0], [10260628712958601000, 0]], [[1.0, 0], [-5994659337.347138, 0], [24417546297445044000, 0]], [[1.0, 0], [26384712111.362385, 0], [243569224216081300000, 0]], [[1.0, 0], [22691654892.97957, 0], [925103102315013600000, 0]], [[1.0, 0], [-1756685022.6338143, 0], [1718264124282290800000, 0]], [[1.0, 0], [-91644571246.02213, 0], [5460999706120583000000, 0]], [[1.0, 0], [17564357735.245506, 0], [26036721925606487000000, 0]], [[1.0, 0], [-303624665503.41656, 0], [104972647676132440000000, 0]], [[1.0, 0], [-125392224046.98766, 0], [161915287432152770000000, 0]], [[1.0, 0], [-229309750201.88397, 0], [548242166610401400000000, 0]], [[1.0, 0], [1771480352560.6484, 0], [1165087474585497600000000, 0]], [[1.0, 0], [666295021751.9948, 0], [1671849507393789000000000, 0]], [[1.0, 0], [-1731915535615.3857, 0], [4668229371502258000000000, 0]], [[1.0, 0], [-1276001498718.5076, 0], [8871870642308873000000000, 0]], [[1.0, 0], [4870029956924.967, 0], [21982145917308330000000000, 0]], [[1.0, 0], [-4889612950355.028, 0], [67302709016557480000000000, 0]], [[1.0, 0], [3699926085323.7847, 0], [113809328043328940000000000, 0]], [[1.0, 0], [-10605889006836.967, 0], [146853371345156440000000000, 0]], [[1.0, 0], [8974067160674.182, 0], [240984500018808100000000000, 0]], [[1.0, 0], [16100933456980.541, 0], [306580461214335500000000000, 0]], [[1.0, 0], [-8203551599815.111, 0], [489801110321660600000000000, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-75-1.1-c13-0-10', 'leading_term': '0.93221117046056372426292926021971', 'load_key': 'CMFs-workshop', 'motivic_weight': 13, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [13], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/75/14/a/i/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [0.9322111704605637, 0.9207801927361466, 0.8868852360266876, 0.8317090649795036, 0.7571860034707396, 0.6659474318104472, 0.5612473092764049, 0.44686950309190143, 0.3270191499529381, 0.20620067477029613, 0.08908543474554854, -0.019627762470548614, -0.11535580659415264, -0.19377450216208256, -0.25095820169472915, -0.28351222438196466, -0.2886945361611524, -0.2645233547888417, -0.20986761062991635, -0.12451753645007183, -0.009233071905610114, 0.13423175651088892, 0.3031297902946768, 0.4937477658898634, 0.701459545819932, 0.9208050606572223, 1.1455938364290523, 1.3690313572317496, 1.5838659095667535, 1.7825529876309492, 1.957433821667888, 2.1009241381544377, 2.205708883823893, 2.264938356877228, 2.2724209982539723, 2.2228080117413516, 2.1117650101033636, 1.9361260290578315, 1.6940255129941546, 1.3850042542468923, 1.0100857571166186, 0.5718200913675702, 0.07429298747397968, -0.47690130549378446, -1.0747240442828714, -1.7107926612710254, -2.375516933178089, -3.058268586360358, -3.7475813770664774, -4.431377825615975, -5.097217987399004, -5.732564933837338, -6.325061014793627, -6.862808500386599, -7.334647872371764, -7.730426867778726, -8.041253381394013, -8.259725515929848, -8.380132431859245, -8.39862019070427, -8.313317498871221, -8.124417131764746, -7.8342098327897345, -7.447068617174843, -6.969382640209101, -6.4094410835537055, -5.7772688387104925, -5.084417088078621, -4.343713164442706, -3.5689752718872327, -2.774698738314842, -1.9757214069718838, -1.1868765295022756, -0.4226420678375486, 0.30320437657539295, 0.9779157274731357, 1.5900816150564416, 2.129901962847515, 2.589420095942076, 2.9627084613011925, 3.2460012530737488, 3.437769637583562, 3.5387368381199367, 3.55183202716934, 3.482083735946372, 3.336455276600512, 3.1236264271669136, 2.8537272979816146, 2.538031826319346, 2.1886196812913337, 1.8180164556474403, 1.4388228331256185, 1.0633439150572106, 0.7032300428121999, 0.36914024838682324, 0.07043890025065086, -0.18506480644996845, -0.3913261169886676, -0.54421589464994, -0.6416086711353383, -0.6834045454064649, -0.6714840618448984, -0.60959742661368, -0.5031916477733193, -0.3591813334845771, -0.1856708770921942, 0.00836247556675536, 0.21341371068132733, 0.4198112020209269, 0.6180811467845077, 0.7993022221958114, 0.9554375971755044, 1.079632095471594, 1.1664634254416102, 1.2121379387143099, 1.2146233099352313, 1.1737127817324202, 1.091018117902213, 0.9698910668223254, 0.8152758605186727, 0.6334979612505678, 0.43199681352693864, 0.21901266357893226, 0.0032394747895960483, -0.20654248951408707, -0.401839797614874, -0.5748095817522302, -0.7185988500063372, -0.8276450503803291, -0.8979248460600067, -0.9271399064851903, -0.9148308673190573, -0.862413384957256, -0.7731333092967002, -0.6519413067851076, -0.5052906562595068, -0.34086527665333827, -0.16724818934664762, 0.006456567515952883, 0.17103319789909976, 0.3175774185388103, 0.43791545906140433, 0.5250001246769915, 0.573265649273738, 0.5789242527895365, 0.5401892736269149, 0.4574124210088787, 0.33312599771297613, 0.1719847647381109, -0.0193936860686613, -0.23268678130966292, -0.4582153326973209, -0.6853704395713314, -0.9031030151826415, -1.1004566223328307, -1.2671215968033904, -1.3939865691954763, -1.4736625816519524, -1.5009551137779742, -1.4732605193677715, -1.3908656255268195, -1.2571325059010787, -1.0785546119685114, -0.8646753895184925, -0.6278660414347538, -0.38296500981487586, -0.14678780243907283, 0.062478272965112526, 0.22597433737192055, 0.3249400629769959, 0.34152454363675605, 0.25960576228362514, 0.06558474249008579, -0.250879923048581, -0.6962304309909984, -1.2724917845712107, -1.9769043516217704, -2.8017286714699714, -3.7342379336401796, -4.756906382545695, -5.847794124080486, -6.981120732598046, -8.128012014592123, -9.257396623109312, -10.337022274636018, -11.334555418381594, -12.218723632560831, -12.960457011267213, -13.533983536259266, -13.91783400765607, -14.095714566053262, -14.05720912468678, -13.798280011288824, -13.32154258438143, -12.636298255983263, -11.758319879399751, -10.70939345706696, -9.516630168365001, -8.21157237685545, -6.829126122551563, -5.406360235167088, -3.9812182608019997, -2.59119358102817, -1.272020200527996, -0.056431556818619416, 1.026962670364927, 1.9546363344312159, 2.708904346971904, 3.278447454284422, 3.6585835134125877, 3.851275253775991, 3.8648757700718654, 3.7136242712332326, 3.4169153977011413, 2.998375218793215, 2.4847853756612572, 1.9049033462030855, 1.2882311601160399, 0.6637868661824509, 0.058932540528247604, -0.5016903686513707, -0.997072911883871, -1.4105597385585373, -1.7303506721863195, -1.9497645750577628, -2.0672587186736138, -2.0862085632990834, -2.0144642538101514, -1.8637107002011772, -1.6486673068446578, -1.3861707852780303, -1.0941896587048279, -0.7908217776723779, -0.4933262729811495, -0.2172388625479149, 0.02438557385026932, 0.22156648254891562, 0.3677996337446115, 0.4602505941715338, 0.49973401188550426, 0.4904846788015953, 0.43973760497914033, 0.3571446435708431, 0.2540639890196818, 0.14276565156269352, 0.03560040929684164, -0.05581849929442543, -0.1213726681379195, -0.15309023134062227, -0.1456536500512548, -0.09673368117178763, -0.00712982068054866, 0.11929110077849588, 0.27585454386630814, 0.45352064219793786, 0.6414828198890757, 0.8278865009963428], 'positive_zeros': ['0.76018872819097900813837134125826', '1.41121534497906276126214097037452', '2.96299652684598594888876457792024', '5.17321737128865217680599933920147', '6.69785691833331156788675291833796', '7.45019853131763193223757799833243', '8.649500959347223138151865359903357', '9.700467607708680593799841834379897', '10.46983793697610532060708087959699', '11.71983123444254421309714350322040'], 'prelabel': '2-75-1.1-c13-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.967898121295455, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c13-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.76018872819097900813837134126', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.41121534497906276126214097037', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.96299652684598594888876457792', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 80.42319671393456, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 75, 'conductor_radical': 15, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/75/14/a/i/1/1'], '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': '2-75-1.1-c13-0-10', 'motivic_weight': 13, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [13], 'order_of_vanishing': 0, 'prelabel': '2-75-1.1-c13-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.967898121295455, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c13-0', 'z1': {'__RealLiteral__': 0, 'data': '0.76018872819097900813837134126', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '963653697578028872713578444383', 'Lhash_array': ['963653697578028872713578444383'], 'factors': ['2-75-1.1-c13-0-10'], 'label': '2-75-1.1-c13-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/14/a/i/1/1'}