-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2212457196814644994246622736797', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': -1, 'a8': 0, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.635718998299005, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, -1]], [37, [1, 1]]], 'bad_primes': [2, 5, 37], 'central_character': '2960.1', 'coefficient_field': '1.1.1.1', 'conductor': 2960, 'conductor_radical': 370, 'degree': 2, 'euler_factors': [[1], [1, -1, 3], [1, -1], [1, 1, 7], [1, -3, 11], [1, 6, 13], [1, 0, 17], [1, 0, 19], [1, 2, 23], [1, 6, 29], [1, 0, 31], [1, 1], [1, 9, 41], [1, -10, 43], [1, 1, 47], [1, -1, 53], [1, 0, 59], [1, 12, 61], [1, 0, 67], [1, -5, 71], [1, -3, 73], [1, 16, 79], [1, 11, 83], [1, 0, 89], [1, -8, 97], [1, 1, 101], [1, -10, 103], [1, 20, 107], [1, 12, 109], [1, -14, 113]], 'euler_factors_factorization': [[1], [[[1, -1, 3], 1]], [[[1, -1], 1]], [[[1, 1, 7], 1]], [[[1, -3, 11], 1]], [[[1, 6, 13], 1]], [[[1, 0, 17], 1]], [[[1, 0, 19], 1]], [[[1, 2, 23], 1]], [[[1, 6, 29], 1]], [[[1, 0, 31], 1]], [[[1, 1], 1]], [[[1, 9, 41], 1]], [[[1, -10, 43], 1]], [[[1, 1, 47], 1]], [[[1, -1, 53], 1]], [[[1, 0, 59], 1]], [[[1, 12, 61], 1]], [[[1, 0, 67], 1]], [[[1, -5, 71], 1]], [[[1, -3, 73], 1]], [[[1, 16, 79], 1]], [[[1, 11, 83], 1]], [[[1, 0, 89], 1]], [[[1, -8, 97], 1]], [[[1, 1, 101], 1]], [[[1, -10, 103], 1]], [[[1, 20, 107], 1]], [[[1, 12, 109], 1]], [[[1, -14, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 64, 'label': '2-2960-1.1-c1-0-64', '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/2960/2/a/h', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.1491915908628339e-60, 0.19874061338488838, 0.3971646085659426, 0.5949029460757709, 0.7914848962074829, 0.9862948193765466, 1.1785374234409034, 1.3672133132356856, 1.5511059760502177, 1.7287806938410564, 1.898595296518151, 2.0587222023767717, 2.2071808383709577, 2.3418792823642667, 2.4606637991941733, 2.561374827016769, 2.6419078874920716, 2.700277826477008, 2.734684731576099, 2.7435798162407594, 2.725729509402301, 2.6802759507941163, 2.6067920731856336, 2.5053294625240285, 2.376457234022337, 2.221290254081708, 2.0415051805375626, 1.8393429910319048, 1.6175969230350185, 1.3795850584368068, 1.1291071474503107, 0.8703856750355791, 0.6079916199089954, 0.34675583086495043, 0.09166743489615539, -0.15223881807894804, -0.38000389417789254, -0.5868716760273248, -0.7684188099966416, -0.9206836601511416, -1.040290587534465, -1.1245656312558594, -1.1716396381615601, -1.18053498112875, -1.1512322294314845, -1.0847134915154957, -0.9829796398772187, -0.8490392438939777, -0.6868677688461642, -0.5013364325449816, -0.2981110246926376, -0.08352196366869322, 0.13559213776042778, 0.35206413411024146, 0.5585970190978374, 0.7479765114816266, 0.9132916890628856, 1.0481571797983278, 1.1469299696367568, 1.2049136412336738, 1.2185428388108703, 1.185540978350184, 1.1050446977326713, 0.9776892686155828, 0.8056501619718459, 0.5926371540863586, 0.3438387517836319, 0.06581626806518556, -0.23365145285961292, -0.5457699312176945, -0.8609731020077649, -1.169203374919632, -1.4602200004928587, -1.7239266654147416, -1.950708111377492, -2.1317647442038794, -2.2594337207387487, -2.3274849079242306, -2.331380426972519, -2.268487237118377, -2.1382333742983244, -1.9422000204056853, -1.6841435023395335, -1.3699435548211882, -1.0074766599655016, -0.6064159198067054, -0.1779616345511662, 0.26549054942842343, 0.7107344950492822, 1.1441796760067142, 1.5523047687326852, 1.92212340624915, 2.2416456983831177, 2.500318627226573, 2.68942854875145, 2.802449795395344, 2.8353247803576345, 2.7866630270096087, 2.6578491352102476, 2.4530527744019257, 2.1791372618906135, 1.8454670240852258, 1.4636181125664645, 1.0469998078053937, 0.6103990370177739, 0.16946270465778152, -0.2598640638013636, -0.6619234675351598, -1.0219324939772636, -1.3265496692891363, -1.5643985824374407, -1.7265266940494872, -1.8067798651190197, -1.8020758192552464, -1.712563303306559, -1.5416579170289897, -1.2959502930155173, -0.9849873461803383, -0.6209324797433871, -0.21811572073762842, 0.20751045325628714, 0.6389895545503972, 1.0590301779157438, 1.4506994380034093, 1.7981127767618323, 2.0870916275593117, 2.3057610729687013, 2.4450614822594066, 2.499151120997755, 2.465680795318982, 2.3459265842046557, 2.1447724360143074, 1.8705406335342225, 1.534674607985477, 1.1512850303437163, 0.7365762437155079, 0.3081756438231249, -0.11560669624270582, -0.5165572581278558, -0.8773439426800355, -1.1822724328379541, -1.4179805071273746, -1.574038851614601, -1.643430469144277, -1.622885668717432, -1.5130556480597404, -1.3185146137907071, -1.047587922495667, -0.712011542239005, -0.3264358751392869, 0.09220571147484397, 0.5254367740140058, 0.9540538117482867, 1.3589820919094773, 1.7221325284724696, 2.0272201924134103, 2.2605061925724836, 2.4114276468925127, 2.4730851649326944, 2.4425635005806914, 2.3210685467787573, 2.1138723017085495, 1.8300664539875227, 1.4821343917027165, 1.085360297597279, 0.6571021147548938, 0.21596214269686959, -0.21910551254734792, -0.6297077597742957, -0.9989011214493778, -1.3120121532885787, -1.5573484425263275, -1.726763748948945, -1.8160475580731221, -1.8251176286485336, -1.7580036577144795, -1.622620505518167, -1.4303400191891034, -1.1953808411916074, -0.9340451587198108, -0.6638396419646965, -0.40252438346465347, -0.16713811498852618, 0.02694993236002771, 0.16691160554619744, 0.2432079423766573, 0.25017240961020465, 0.18639559832466535, 0.054887353823471104, -0.13699658696029066, -0.3778643708587061, -0.652822818906339, -0.9442138355169879, -1.2325179909871455, -1.4973813285013096, -1.7187140197375577, -1.8778045780280672, -1.958391250116591, -1.947633122222123, -1.8369274159267635, -1.6225262789813442, -1.3059158051901933, -0.8939316122207591, -0.39859850820757375, 0.16330406898816938, 0.7709347742908889, 1.4003113152398527, 2.0254171303677238, 2.619440629932841, 3.1560857671362794, 3.610887677120592, 3.9624654676394657, 4.1936461300086645, 4.292398937905523, 4.252528403174287, 4.074085469613709, 3.7634705913893893, 3.3332179679542016, 2.801466694195169, 2.1911410718900313, 1.5288779373301429, 0.8437527400522784, 0.16586748457247255, -0.4751281343701375, -1.0515065101115115, -1.5388463267675212, -1.917258168764589, -2.1723859419403295, -2.296129550510398, -2.287048394692956, -2.1504217414879894, -1.8979600204664042, -1.5471796542681036, -1.1204721496257355, -0.6439148560910278, -0.1458851153587113, 0.3444493419367882, 0.7986835968138221, 1.190689174862865, 1.4980064473322374, 1.7030401238370991, 1.793992360815239, 1.7654819113511264, 1.6188146181916223, 1.361889499818926, 1.0087446675862455, 0.5787672355838268, 0.09561012789082704, -0.414124814641328, -0.922364726172965, -1.4011225860622967, -1.8240462785291531, -2.167873150141984, -2.4137083798646066, -2.5480551549615225, -2.5635384892157775, -2.4592817746472133], 'positive_zeros': ['1.74532098704194312687928737334999', '2.60923523958215693481233001489710', '3.41377076281611111322968390654453', '4.38768963429872255146818666899854', '5.35180875187622235918959951271991', '6.06920600436887629708345648593489', '6.94299637524333632172982066183201', '7.60623153841211391363563986698926', '8.454669908512517207034899469370386'], 'prelabel': '2-2960-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.861658050325938, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1990631071015422612, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.74532098704194312687928737335', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.60923523958215693481233001490', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.41377076281611111322968390654', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 23.635718998299005, 'bad_primes': [2, 5, 37], 'central_character': '1.1', 'conductor': 2960, 'conductor_radical': 370, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 1, 0, -1, 0, -2, 0, 3, 0, -6, 0, 1, 0, 0, 0, 0, 0, -1, 0, -2, 0, 1, 0, -5, 0, -6, 0, 0, 0, 3, 0, -1, 0, -1, 0, -6, 0, -9, 0, 10, 0, -2, 0, -1, 0, -6, 0, 0, 0, 1, 0, 3, 0, 0, 0, 0, 0, -12, 0, 2, 0, -6, 0, 0, 0, -2, 0, 5, 0, 3, 0, 1, 0, -3, 0, -16, 0, 1, 0, -11, 0, 0, 0, -6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 8, 0, -6, 0], 'euler11': [1, -3, 11], 'euler13': [1, 6, 13], 'euler17': [1, 0, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, 2, 23], 'euler29': [1, 6, 29], 'euler3': [1, -1, 3], 'euler31': [1, 0, 31], 'euler37': [1, 1, 0], 'euler41': [1, 9, 41], 'euler43': [1, -10, 43], 'euler47': [1, 1, 47], 'euler5': [1, -1, 0], 'euler53': [1, -1, 53], 'euler59': [1, 0, 59], 'euler61': [1, 12, 61], 'euler67': [1, 0, 67], 'euler7': [1, 1, 7], 'euler71': [1, -5, 71], 'euler73': [1, -3, 73], 'euler79': [1, 16, 79], 'euler83': [1, 11, 83], 'euler89': [1, 0, 89], 'euler97': [1, -8, 97], 'euler_factors': [[1, 0, 0], [1, -1, 3], [1, -1, 0], [1, 1, 7], [1, -3, 11], [1, 6, 13], [1, 0, 17], [1, 0, 19], [1, 2, 23], [1, 6, 29], [1, 0, 31], [1, 1, 0], [1, 9, 41], [1, -10, 43], [1, 1, 47], [1, -1, 53], [1, 0, 59], [1, 12, 61], [1, 0, 67], [1, -5, 71], [1, -3, 73], [1, 16, 79], [1, 11, 83], [1, 0, 89], [1, -8, 97]], 'index': 64, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/2960/h', 'ModularForm/GL2/Q/holomorphic/2960/2/a/h/1/1', 'ModularForm/GL2/Q/holomorphic/2960/2/a/h'], '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': '2-2960-1.1-c1-0-64', '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': '2-2960-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.861658050325938, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1990631071015422612, 'z1': {'__RealLiteral__': 0, 'data': '1.74532098704194312687928737335', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20476155
{'Lhash': '2212457196814644994246622736797', 'Lhash_array': ['2212457196814644994246622736797'], 'factors': ['2-2960-1.1-c1-0-64'], 'label': '2-2960-1.1-c1-0-64', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2960/2/a/h'}
-
id: 24559543
{'Lhash': '2212457196814644994246622736797', 'Lhash_array': ['2212457196814644994246622736797'], 'factors': ['2-2960-1.1-c1-0-64'], 'label': '2-2960-1.1-c1-0-64', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2960/2/a/h/1/1'}
-
id: 25235
{'Lhash': '1990631071015422612', 'Lhash_array': ['1990631071015422612'], 'factors': ['2-2960-1.1-c1-0-64'], 'label': '2-2960-1.1-c1-0-64', 'type': 'ECQ', 'url': 'EllipticCurve/Q/2960/h'}