-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2467263489432025479163390496928', 'a10': [1300.2908262418018, -1036.9473317357508], 'a2': [-4.853038532388947, 10.077438350895658], 'a3': [-1.6330335380009242, -1.302300789708219], 'a4': [1.803913918667148, 2.262036506566308], 'a5': [-133.96667032043152, -64.51494819247567], 'a6': [21.049030607209243, -10.136678890934794], 'a7': [-384.8624068857237, 482.60219369210307], 'a8': [-1427.3488577854148, 325.7830624677551], 'a9': [-485.68247137309845, -2127.913942209331], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.059165739039535, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[29, [[1.0, 0], [36906.216171361506, -126046.84651712923]]]], 'bad_primes': [29], 'central_character': '29.13', 'coefficient_field': 'CDF', 'conductor': 29, 'conductor_radical': 29, 'conjugate': '145247884995805361769725090264', 'degree': 2, 'euler_factors': [[[1.0, 0], [4.853038532388947, -10.077438350895658], [-79.80669463791789, -100.07442975590781]], [[1.0, 0], [1.6330335380009242, 1.302300789708219], [486.6532825624596, 2132.167343941648]], [[1.0, 0], [133.96667032043152, 64.51494819247567], [48710.140770213555, 61080.584567814825]], [[1.0, 0], [384.8624068857237, -482.60219369210307], [-183255.55751318502, -802895.0575819556]], [[1.0, 0], [-533.68661038637, -121.81048619008739], [17557334.394490853, 8455166.618303245]], [[1.0, 0], [-1395.833746842629, 6115.547226803288], [-56534460.3240457, -27225561.18004166]], [[1.0, 0], [0, 26867.646790477444], [-410338673.0, 0]], [[1.0, 0], [-2844.3680836120325, 2268.3078548670364], [198905174.1994349, -871460508.261606]], [[1.0, 0], [72189.12271991324, -34764.44925589213], [2122873943.3136039, -2661999726.7728825]], [[1.0, 0], [36906.216171361506, -126046.84651712923]], [[1.0, 0], [82538.5150927468, -171392.99263139747], [-17153834320.683186, -21510227876.973965]], [[1.0, 0], [52120.191495949, -11896.093592915346], [85530665868.37056, -41189397811.91465]], [[1.0, 0], [0, 477314.222043653], [-194754273881.0, 0]], [[1.0, 0], [-105351.02232642577, -218763.65201159305], [-169476131980.61957, 212516347684.18668]], [[1.0, 0], [973639.6040927139, 222226.88604197107], [456451659296.74, 219815533829.8915]], [[1.0, 0], [1049018.4511929967, 505180.6607553315], [732420415818.2181, 918426151930.4708]], [[1.0, 0], [90709.3730969113, 0], [2488651484819.0, 0]], [[1.0, 0], [-1895063.5105048541, -1511262.7198696912], [699326071055.9092, 3063947711646.337]], [[1.0, 0], [-54501.5441647117, -238786.86700829404], [-5460512473730.917, 2629644213030.721]], [[1.0, 0], [215967.26709941938, -946214.4215797114], [-8194420112542.01, -3946224742046.1646]], [[1.0, 0], [-368349.7300632824, -764886.0958980503], [-6887940313726.255, 8637203961600.725]], [[1.0, 0], [2154287.884278523, -491702.15154433536], [17302124138560.768, -8332263836587.941]], [[1.0, 0], [718304.4440298368, 900725.2831802749], [-6038339410097.97, 26455693536176.56]], [[1.0, 0], [106790.1761874728, -221752.0857970169], [-27577786229960.664, -34581450132911.336]], [[1.0, 0], [-9576864.843169, 7637294.861350736], [17979309724137.688, -78772502794119.75]], [[1.0, 0], [6856392.847934267, 14237446.452041045], [-66846545825094.32, 83822917174420.67]], [[1.0, 0], [-1397599.7086115412, 6123284.410850416], [-110807806419461.73, -53362227137350.71]], [[1.0, 0], [1454267.7311874572, 6371563.23997063], [-144675911896144.62, 69672247122017.44]], [[1.0, 0], [1989226.6452341224, -2494411.3157454277], [-40677697247280.97, -178220636344451.2]], [[1.0, 0], [5934338.93569569, 4732477.38182604], [52350396874007.055, 229362074924085.03]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-29-29.13-c7-0-10', 'load_key': 'CMFs-workshop', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/29/8/e/a/13/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [0.2152395409103287, 0.5078428322742142, 0.7469621581763924, 0.9252097716769901, 1.0371373907317751, 1.0794559604430167, 1.0512865201926977, 0.9544256612981341, 0.793597665013262, 0.5766552807939365, 0.31468334840585116, 0.02195524879559625, -0.28430736291445197, -0.5844149081407758, -0.8569610381071573, -1.079855889297647, -1.23162687818586, -1.292941301261402, -1.248270588341202, -1.0875814142166365, -0.807907899581281, -0.41463635350405986, 0.0776758157602767, 0.6451178343081905, 1.255022374650824, 1.8674329841244373, 2.437460980106312, 2.9184598814357887, 3.265843506982375, 3.441270827600763, 3.4168290665485626, 3.1787803473061054, 2.730410095398805, 2.0935389062293677, 1.3083408342222382, 0.43125082190585, -0.46906482872176963, -1.3174741049029957, -2.0394413076812565, -2.5687249220070063, -2.854881374231039, -2.869658699528235, -2.6113873324180896, -2.1066220604528065, -1.4085583310732945, -0.5921178002467959, 0.2539662598465559, 1.0372878780346977, 1.6729659055200437, 2.094466175031941, 2.262525270280401, 2.1707808524289876, 1.8470672499662064, 1.3498881022540492, 0.7602674687849715, 0.16991284508723578, -0.3327162439418042, -0.6763696222276759, -0.8187532179020781, -0.7539917088295413, -0.514279312760157, -0.1650479533742367, 0.20595945312360023, 0.5042267594192698, 0.646186994164765, 0.5761006011512236, 0.2789453879355816, -0.21337960850831555, -0.8242474558818227, -1.4432032857660777, -1.9442821187003514, -2.208942353021874, -2.1496811293548785, -1.7299049586149067, -0.9759363103309432, 0.02183310543513174, 1.1198157746507937, 2.143087677518311, 2.914977048677868, 3.2893481350593903, 3.179600522536033, 2.578559575543127, 1.5647578768880819, 0.2929383108346109, -1.030438652177705, -2.1828771226891157, -2.9664293279325715, -3.24550768651711, -2.974337196857889, -2.20810716648101, -1.094860223971923, 0.15106669989538662, 1.289406661603634, 2.1004236190757513, 2.4281643635554975, 2.2115025109394253, 1.4962302609386529, 0.42527081007888645, -0.7912960803952614, -1.9202693780584006, -2.7540559570751055, -3.153470900835464, -3.075095579491238, -2.5770053941203437, -1.8015422302092876, -0.9391288594076018, -0.18165771574103, 0.32338739781895154, 0.5069176152035162, 0.3919092999085387, 0.08324366967326721, -0.2638483894793484, -0.488763866673812, -0.4722601999708468, -0.17245670090647022, 0.3599737655473494, 0.9923344256268684, 1.5443551754740927, 1.8381982426055394, 1.7509876722463908, 1.2554212420939157, 0.4364385415405047, -0.522260292947507, -1.380187025635805, -1.900966079385041, -1.9167977565338186, -1.379128775609724, -0.3807855777744939, 0.8583800128045275, 2.0408913895434697, 2.86506186729482, 3.104208010454882, 2.670780585861182, 1.6473847280098861, 0.2745750553188447, -1.1035904909710903, -2.123836942907101, -2.496774733136362, -2.0844760173332415, -0.9413404726761451, 0.6938684535932765, 2.4542039799859166, 3.935290554359578, 4.797283717333496, 4.85106872127159, 4.1054731715384545, 2.7625311194709843, 1.1619186106178598, -0.31029629142751314, -1.3234673261863457, -1.6866289111158537, -1.3920618213323654, -0.6066831220556655, 0.38518290213871825, 1.2700397139195942, 1.7979439308238965, 1.852174784922759, 1.4755422579604907, 0.8464374190271373, 0.21327032484011305, -0.1911606455833517, -0.22762477711844156, 0.1044565145649497, 0.66936791453648, 1.2440195308069988, 1.597149580402291, 1.5721969913973461, 1.1454693384596681, 0.43887619129321837, -0.31867604931973414, -0.8697977390989422, -1.0214536587267002, -0.720436089435356, -0.08413518954318952, 0.6268975475902179, 1.0889652448964597, 1.0239260297787618, 0.30146206841044276, -1.0002321763940103, -2.5987261003785473, -4.079712933137752, -5.0181216873589545, -5.111377343541676, -4.282126475908003, -2.715443587608327, -0.8151326388530065, 0.9106845885869884, 2.001127462342003, 2.1843339201724445, 1.4639859000215918, 0.12147109743091836, -1.36904106725026, -2.4872887263443415, -2.8295620683822618, -2.235530714253862, -0.8383711127662035, 0.9781971679469642, 2.702149804906835, 3.8549088289747147, 4.139896360781746, 3.5297201502501374, 2.264468692104965, 0.7634633909743478, -0.5182192128392387, -1.2389951619903026, -1.2752582798988243, -0.7469342825565904, 0.04200133886659445, 0.7242710065934909, 1.0064278486476232, 0.7726509275293687, 0.11860053351835942, -0.694979826964607, -1.3493912447363914, -1.593921497724516, -1.3420769591466224, -0.7013082259721057, 0.0747827936056101, 0.6925728561133925, 0.9405908664130992, 0.7784435076421107, 0.35539493759106283, -0.051335036529326084, -0.15648724148884746, 0.20167230351863216, 0.9718137170386308, 1.881893105232386, 2.5229669531351737, 2.4983175750955198, 1.5842085075277874, -0.15962764858633116, -2.376391611045122, -4.508036907848744, -5.972240585217509, -6.360027927801525, -5.582568686014495, -3.9110693177982054, -1.8908094687725532, -0.1560972295890753, 0.7896392759956207, 0.7496167309051357, -0.09952897722406326, -1.2761394046850052, -2.173946423352779, -2.2895886413491056, -1.4139754801867166, 0.2833487412584766, 2.3086870300569307, 4.018082633819213, 4.846818249921043, 4.510074105407843, 3.1013276886203744, 1.0536924945086403, -1.0190906808639122, -2.5405758246478767, -3.1661948863404263, -2.8831723066321167], 'positive_zeros': ['1.94632770969209991370170410290936', '3.84137437580365796196763192971891', '6.23622207166141614304825011810161', '8.032668118080785482330983939332160', '9.722769565917779873363420185911504', '10.79946706076985288375820257163120', '11.70805425251826588870160878170134', '13.18002116249571121747183159577118', '14.62830977546230257559270978284672', '15.97464580401500514885255093805260'], 'prelabel': '2-29-29.13-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0098448031484173, 'root_angle': 0.521845338520121, 'root_number': '-0.06857529425601311 + 0.997645943718362*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.26092266926', 'prec': 44}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.94632770969209991370170410291', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.84137437580365796196763192972', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.23622207166141614304825011810', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 9.059165739039535, 'bad_primes': [29], 'central_character': '29.13', 'conductor': 29, 'conductor_radical': 29, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/29/8/e/a/13/6'], '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': '2-29-29.13-c7-0-10', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-29-29.13-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0098448031484173, 'root_angle': 0.2609226692600605, 'self_dual': False, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '1.94632770969209991370170410291', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2467263489432025479163390496928', 'Lhash_array': ['2467263489432025479163390496928'], 'label': '2-29-29.13-c7-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/29/8/e/a/13/6'}