-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '699897871646189530684344047088', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-4.417765132219055, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 66.11613287362019, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [23, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '8280.1', 'coefficient_field': 'CDF', 'conductor': 8280, 'conductor_radical': 690, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [4.417765132219055, 0], [7.0, 0]], [[1.0, 0], [0.24559781783331783, 0], [11.0, 0]], [[1.0, 0], [-0.7256296977682318, 0], [13.0, 0]], [[1.0, 0], [0.7373394907870052, 0], [17.0, 0]], [[1.0, 0], [-1.7544021821666822, 0], [19.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [10.225846889280948, 0], [29.0, 0]], [[1.0, 0], [3.462969188555237, 0], [31.0, 0]], [[1.0, 0], [-0.2736774446514815, 0], [37.0, 0]], [[1.0, 0], [-6.361544140444387, 0], [41.0, 0]], [[1.0, 0], [-1.0287724843984503, 0], [43.0, 0]], [[1.0, 0], [-3.898489869734256, 0], [47.0, 0]], [[1.0, 0], [5.126963258049556, 0], [53.0, 0]], [[1.0, 0], [-3.6921354344508237, 0], [59.0, 0]], [[1.0, 0], [9.328049877126979, 0], [61.0, 0]], [[1.0, 0], [-8.56185281978663, 0], [67.0, 0]], [[1.0, 0], [2.720907918849274, 0], [71.0, 0]], [[1.0, 0], [-13.282760738635902, 0], [73.0, 0]], [[1.0, 0], [13.082452059293662, 0], [79.0, 0]], [[1.0, 0], [16.29595803611389, 0], [83.0, 0]], [[1.0, 0], [-14.197767262462785, 0], [89.0, 0]], [[1.0, 0], [-18.6777991423977, 0], [97.0, 0]], [[1.0, 0], [-2.2861651774054352, 0], [101.0, 0]], [[1.0, 0], [3.405970257045388, 0], [103.0, 0]], [[1.0, 0], [-1.955488801244105, 0], [107.0, 0]], [[1.0, 0], [-13.705247649773916, 0], [109.0, 0]], [[1.0, 0], [2.3902315426879435, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-8280-1.1-c1-0-15', 'leading_term': '1.348098918767015762098504446574', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/8280/2/a/bu/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [1.3480989187670158, 1.3380783258376723, 1.3080184652305074, 1.257931471365889, 1.1878583890815528, 1.0978988868735078, 0.9882499606154006, 0.8592510385590594, 0.7114325406821506, 0.5455647936305603, 0.36270423716096856, 0.1642340452379805, -0.0481034146963201, -0.27218448488350633, -0.5054942629221196, -0.7451301270121107, -0.9878196260427005, -1.2299531663813477, -1.4676314751409676, -1.6967273701338608, -1.9129609210134195, -2.1119866471354807, -2.2894909705962325, -2.441297735391245, -2.5634792257046555, -2.652469779889708, -2.7051788149175904, -2.7190998626537874, -2.6924120877134574, -2.6240707192406068, -2.5138828963203976, -2.3625656069034067, -2.171782697950369, -1.944158351127725, -1.6832649507784256, -1.3935839115960356, -1.0804387703993736, -0.7499006630462557, -0.40866718290570353, -0.06391652655262685, 0.2768602527799049, 0.6060451737973801, 0.9160928956675805, 1.1997386432781303, 1.4502085883779894, 1.6614263222390926, 1.8282087737079757, 1.946444849697502, 2.013250220869626, 2.027092054326892, 1.9878781107456764, 1.8970054703532457, 1.7573652164529538, 1.5733006638477531, 1.3505181407357763, 1.0959508764585664, 0.8175781665584656, 0.5242036275760106, 0.22519795905726092, -0.06978686106484452, -0.35112367006088285, -0.6095270900357677, -0.8363710963705246, -1.0239963625520219, -1.1659963720591333, -1.2574714874724233, -1.295240768122427, -1.2780023313159832, -1.2064344441292472, -1.083231282880792, -0.9130693601325351, -0.7025029341412926, -0.45978920958601, -0.19464672645214864, 0.0820470769977724, 0.35861064967103196, 0.6229546901071409, 0.8630073163129655, 1.0671536625316758, 1.2246743806807914, 1.3261669187495397, 1.363933429167301, 1.3323197562099522, 1.2279911691273933, 1.0501323286350845, 0.800561355468701, 0.4837507430033931, 0.10675113050427679, -0.32098248219529374, -0.7878587725893998, -1.280505335157229, -1.7842004563711469, -2.2833674227562453, -2.7621144495256784, -3.2048009680417766, -3.5966093401904424, -3.9241001721606197, -4.175729346696186, -4.342305717225832, -4.417370109957371, -4.39747882497293, -4.282378141710817, -4.075060309742554, -3.7816960019090176, -3.4114430554026343, -2.9761363372986605, -2.489868539907895, -1.968476427455334, -1.4289513109092467, -0.8887961259887921, -0.3653542549817765, 0.12486298012269882, 0.5668225267057441, 0.9475623411365423, 1.2567051138934833, 1.48687020092877, 1.6339648031782834, 1.6973401794247889, 1.6798041645208965, 1.587487277440818, 1.4295659930310496, 1.21785304806545, 0.9662706771758078, 0.6902281510930254, 0.4059296574737614, 0.12964219032208027, -0.12304449595040604, -0.3379328012814088, -0.5028744517102216, -0.6083392577932728, -0.6478681717448198, -0.6183880651538253, -0.5203715080633117, -0.3578316013359325, -0.13814931095399977, 0.12826154938026, 0.4284388909295808, 0.7474864362710788, 1.0692907864925036, 1.3773095236521857, 1.6553943521108858, 1.8886108213413042, 2.0640154611608637, 2.171352279429924, 2.203633519003784, 2.1575742549387886, 2.0338566589241545, 1.837207310150801, 1.5762794648550549, 1.263341328634052, 0.9137806846067874, 0.5454452743185603, 0.17784666496572346, -0.16873745415599647, -0.47422189839536616, -0.719689004734454, -0.8883336748301423, -0.9663324438551812, -0.9435931716736254, -0.8143467119349889, -0.5775486575098204, -0.23706770669803467, 0.19835302794454682, 0.7153647845278257, 1.2965039628812467, 1.9208860617961137, 2.5650736215953014, 3.2040800605102833, 3.8124639843448, 4.365463320602935, 4.840115785374127, 5.216311926384933, 5.477729366587364, 5.612601835928941, 5.614283929538333, 5.4815819485894375, 5.21883223400757, 4.835720568947497, 4.3468489116833515, 3.771068295040404, 3.130608552809895, 2.4500459936428527, 1.755158681750896, 1.0717251315909644, 0.42432562434695936, -0.16479421418285992, -0.6767405441831668, -1.0968176877476299, -1.4151605721485765, -1.6271206803097151, -1.7333853840305449, -1.7398241691868908, -1.6570693993061523, -1.4998531705520324, -1.2861347516857506, -1.0360643789031008, -0.7708381648721051, -0.511505071273267, -0.2777899119846533, -0.08699598978928949, 0.046952809489272274, 0.11427768500794476, 0.1098755500202825, 0.033584243196331826, -0.10983382589153566, -0.3109904493362753, -0.5564381180905353, -0.8294745985174771, -1.111142411671427, -1.381368692021404, -1.6201823989806936, -1.8089407093073562, -1.931494970848771, -1.9752289905312712, -1.9319085950614736, -1.7982910648824004, -1.5764557251974107, -1.2738320306451247, -0.9029181070099283, -0.480700016248009, -0.027799037605948693, 0.43260994734637875, 0.876052218712773, 1.2781116629162794, 1.6158192990948774, 1.8689942127739638, 2.021460447278437, 2.0620689376644554, 1.9854631826427502, 1.7925405705073467, 1.4905774271581655, 1.0930040819587716, 0.6188355617317715, 0.09178285665041164, -0.46091203425528054, -1.0098579232419798, -1.525040681106765, -1.977412241848812, -2.340455901268231, -2.591641432657461, -2.7136883870332564, -2.6955654496372827, -2.533167422442503, -2.229628581222211, -1.7952508923109016, -1.247046784625179, -0.6079176716126298, 0.09449001450687948, 0.8291910627705118, 1.563454531310848, 2.2644969950097615, 2.9011830448214004, 3.4456389746079266, 3.8746898263284013, 4.171039369368342, 4.324126681475911, 4.330611015332105], 'positive_zeros': ['0.55212206858907260519352753040321', '1.83684426880189937497365115176221', '2.75439491999202419768320496715013', '3.45493870074482052559131606654329', '4.09031111654381802645672123338038', '5.19079379506193749077673212604520', '5.88270530532947663223530817400701', '6.30644332886207574820135050979386', '7.14852608312616589903707621897267', '7.57356804002162474255250513350800'], 'prelabel': '2-8280-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.131182747523278, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.55212206858907260519352753040', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.83684426880189937497365115176', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.75439491999202419768320496715', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 66.11613287362019, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 8280, 'conductor_radical': 690, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8280/2/a/bu/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': '2-8280-1.1-c1-0-15', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-8280-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.131182747523278, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.55212206858907260519352753040', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '699897871646189530684344047088', 'Lhash_array': ['699897871646189530684344047088'], 'label': '2-8280-1.1-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8280/2/a/bu/1/1'}