-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2102930909936253788265213426118', 'a10': [-0.3917008076667577, 0.4520468296899063], 'a2': [-0.12902385117426243, 0.08291859427367282], 'a3': [0.9898214418809327, 0.14231483827328514], 'a4': [-0.8210583651082566, 1.797867037974746], 'a5': [3.742003725174911, -1.0987514303854131], 'a6': [-0.13951112074024521, 0.06371259402944532], 'a7': [2.5915927866618893, 0.5325850430889546], 'a8': [-0.08679441827081308, -0.6036684388107117], 'a9': [0.9594929736144974, 0.28173255684142967], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.9898214418809327, -0.14231483827328514]]], [7, [[1.0, 0], [-2.5915927866618893, -0.5325850430889546]]], [23, [[1.0, 0], [1.4748957856504992, 4.563406887564421]]]], 'bad_primes': [3, 7, 23], 'central_character': '483.34', 'coefficient_field': 'CDF', 'conductor': 483, 'conductor_radical': 483, 'conjugate': '2248204817613429350079611558833', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.12902385117426243, -0.08291859427367282], [0.8308300260037729, -1.8192639907090367]], [[1.0, 0], [-0.9898214418809327, -0.14231483827328514]], [[1.0, 0], [-3.742003725174911, 1.0987514303854131], [4.206267664155906, -2.703204087277988]], [[1.0, 0], [-2.5915927866618893, -0.5325850430889546]], [[1.0, 0], [-0.1708297020096642, 0.2658162049333814], [-4.569565143020751, -10.005951948899702]], [[1.0, 0], [1.1492079835497706, 0.9957943862637433], [1.850092897552707, 12.867678744452126]], [[1.0, 0], [2.426910784347795, 5.31419334934739], [-11.132632477069846, 12.84774276402239]], [[1.0, 0], [3.191639174776506, -6.988714948032987], [-12.442353944960416, -14.359241912730907]], [[1.0, 0], [1.4748957856504992, 4.563406887564421]], [[1.0, 0], [-2.1992802289271167, -4.815751959772409], [-18.990961284413267, 21.91673765627349]], [[1.0, 0], [4.534704148334511, -0.6519920262194645], [29.744282182049417, -8.73370926208432]], [[1.0, 0], [-0.7898946541321986, 2.6901341436448662], [-31.126380714753704, -20.00371024585711]], [[1.0, 0], [-2.2110975298185327, -7.53030664124252], [-34.49139484607843, 22.1662735156795]], [[1.0, 0], [7.047096440577042, 1.013219503844216], [41.25819786542339, 12.114499944181476]], [[1.0, 0], [0, -8.318292149031192], [-47.0, 0]], [[1.0, 0], [0.23753028597495898, -0.20582116442566628], [7.542686428484113, -52.46053641968943]], [[1.0, 0], [0.835724764445605, 0.724159630640506], [8.396575458123824, 58.39946507097503]], [[1.0, 0], [0.5911319745947959, 4.111413191586921], [-58.52907139048434, 17.185685967327213]], [[1.0, 0], [7.912519834034676, 12.312121188528556], [-27.83280587112639, 60.94534368875273]], [[1.0, 0], [1.3862144556665645, -0.8908659366435405], [29.494465923133937, -64.58387167017081]], [[1.0, 0], [8.128852997819736, 3.7123227756117156], [47.80483357800581, 55.169718927860856]], [[1.0, 0], [-3.6623861802727147, -3.1734756900838543], [11.242872223589526, 78.19589390859369]], [[1.0, 0], [-5.942894072680331, -1.7449911444653325], [69.82404322498803, 44.8731878488146]], [[1.0, 0], [1.0821009630302332, -7.526177512358472], [-85.39487465169027, -25.074197558887242]], [[1.0, 0], [18.197953527425856, -5.343401272913433], [81.60159268462458, -52.442159293192965]], [[1.0, 0], [-3.311435118142398, 11.27771232426728], [-84.9666068159493, -54.60472256301536]], [[1.0, 0], [-5.192844565365833, -3.3372385626612635], [42.7877463391943, 93.6920955215154]], [[1.0, 0], [-1.7758151520599073, 0.2553236730135976], [102.66574817675122, -30.145383582032977]], [[1.0, 0], [-8.57293378583197, 3.9151276761298552], [71.37982000003608, -82.37670360461415]], [[1.0, 0], [9.35372793744245, 14.554684771209384], [-46.94189646921317, 102.78841547506057]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 22, 'label': '2-483-161.34-c1-0-22', '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/483/2/r/a/34/16', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.0412489318235387, 2.0028747574882195, 1.9634861926611131, 1.9172405021873398, 1.8562968075563917, 1.7723102285912582, 1.6578952335484194, 1.5079066871131053, 1.3204868364536593, 1.097860448974283, 0.8468477582403483, 0.579039585995594, 0.31056412711508313, 0.06138030646821309, -0.14594002001381337, -0.28793197866118286, -0.34238941063804545, -0.29080921800824616, -0.12092111697318565, 0.1709615840039936, 0.5780704604123255, 1.0820948244510977, 1.6531502795057225, 2.2509980646340124, 2.827593014387539, 3.330887270037975, 3.709646792735056, 3.9188680084498673, 3.9252363016258327, 3.7119715377876457, 3.282380988979338, 2.6615033796400254, 1.8953857089069854, 1.0477805952673078, 0.1943653663282714, -0.5850695253420151, -1.2156812865561413, -1.6368328644266836, -1.8103390472963716, -1.7264870948144027, -1.4067900055613254, -0.9027766966255569, -0.29061535813289935, 0.33805181133355333, 0.8880904214401394, 1.2741851602365963, 1.4336476080106382, 1.3367861328024253, 0.9930911726002339, 0.4519697436579067, -0.20250799748774195, -0.8625006999450685, -1.4116604485072455, -1.7427057064572888, -1.7747018598965458, -1.4672902284607257, -0.829389390486402, 0.07938882467089153, 1.1552943470246342, 2.2643771411115305, 3.2619485855976733, 4.014656055610818, 4.42163656691974, 4.431161660413103, 4.049757506941427, 3.3419273457011847, 2.420154233862978, 1.4265679685704085, 0.5092185137632025, -0.20298996873385108, -0.6222240479668137, -0.7164105348716626, -0.5137756425070898, -0.09611800539733728, 0.4181886690472735, 0.8984348397817954, 1.2284783649490882, 1.3310054883775058, 1.1841339595297158, 0.8266590953557994, 0.3503852361532105, -0.11943123039765022, -0.4519762407081808, -0.541616931496958, -0.3350734476574044, 0.15102547755371398, 0.8266008500815977, 1.540314922797898, 2.1060063523349912, 2.3387826745485665, 2.0938606746031154, 1.3002365891538687, -0.018130841176904056, -1.7387612589991497, -3.6564666983004894, -5.516347385497824, -7.058097563342515, -8.063132851341404, -8.395115075744556, -8.025480006774606, -7.03843616418461, -5.61405664303335, -3.992676449350985, -2.4278431904396687, -1.1376357518579334, -0.2646398309769264, 0.14692703629680642, 0.1521840657823566, -0.11522063470836853, -0.48061190355143424, -0.7735263030135828, -0.8698711831697666, -0.7208427330456603, -0.36153640047363156, 0.10294292379901104, 0.5305237048663985, 0.786130770081341, 0.7853218316430339, 0.5260222168699741, 0.09933142583014891, -0.3247046565098704, -0.5342848205718419, -0.3279786200869098, 0.4304854101449507, 1.768435969835678, 3.583204679567118, 5.650572151138508, 7.662606654818965, 9.287602584262615, 10.239103114694805, 10.338213239393577, 9.554386776938648, 8.014509875259566, 5.977389508506141, 3.778971329644292, 1.7607434713984371, 0.19802098462956, -0.7549894484558879, -1.0904254215352593, -0.9366442897433922, -0.5158421404842497, -0.08058750558426929, 0.15426984856332637, 0.06675530133579154, -0.34412558654885433, -0.9642932132235333, -1.6024275347079386, -2.0490828546132174, -2.14064927460542, -1.8103146728226949, -1.1116067551833397, -0.20751940401801452, 0.6722957915770834, 1.2948204563256691, 1.4900092369524616, 1.2014817246269907, 0.50679489587006, -0.3993181640770816, -1.2551301277095357, -1.8024156289042577, -1.8580801257281105, -1.366888805824126, -0.420029994633476, 0.7665450639399831, 1.9088856310673723, 2.731743646532668, 3.0440237836031994, 2.791615417878062, 2.072143170648186, 1.1066527189666968, 0.1754488783883456, -0.4642183951421438, -0.6552266567142971, -0.38988609997845414, 0.18366441113810078, 0.8011375708202636, 1.157770875218909, 0.9991710404188288, 0.2014614679956531, -1.1828582232314897, -2.927772625501179, -4.686173630195274, -6.078479114117287, -6.79334909997169, -6.672349396778711, -5.754380576260701, -4.26671384717301, -2.5645068374304514, -1.0354197499443112, 0.0038881061582720497, 0.39007716280775806, 0.1509294160947726, -0.5118613997068813, -1.2893933814714158, -1.8617448334098434, -1.9949881087623202, -1.610200449238605, -0.8040918554080925, 0.18452001267496437, 1.051740101064386, 1.5252222916458524, 1.4504520902346811, 0.8398687663539193, -0.13057155264139078, -1.1765022368399831, -1.9948595922774779, -2.360114230070944, -2.1965656202449386, -1.6034157279882906, -0.8239524586449269, -0.16776655609821123, 0.08999289159960304, -0.19944169215251376, -1.004928475422353, -2.1183102795765394, -3.2141832706299005, -3.9489188291614097, -4.068453057723988, -3.490902540789525, -2.3373165109738467, -0.8997539329197055, 0.44449534314449907, 1.3465192804930877, 1.5919454654282879, 1.1661886318481225, 0.2578124397939541, -0.8015895859372244, -1.6424207495191891, -1.9739402562952937, -1.675795980870355, -0.8348835963879537, 0.28445284735570875, 1.3274294704602667, 1.96498011327478, 2.00130992910385, 1.4376060922160807, 0.47074219404171896, -0.5729941037578772, -1.3476669466586977, -1.6048154100289351, -1.2788881925686455, -0.5119310614733477, 0.39174124022769596, 1.0669589173035487, 1.2123046832789495, 0.6966715669571426, -0.3882485085979192, -1.7482664618764876, -2.974686301998265, -3.672357712687855, -3.5864627147723946, -2.686529990999757, -1.1797703784853992, 0.5511503078159374, 2.065918154596226, 3.0015670239235006, 3.1805628784715023], 'positive_zeros': ['1.65891998122955921278171525446506', '2.30822043262098086747536071186289', '4.27962647765360523109404291845039', '5.30703846891032559212362110623555', '6.21243187903147885827952463476664', '7.11513460566476274156495294719154', '8.584294012026350702338830548439600', '9.149210285090619345571808760163531', '10.09101486119459616216870450437773', '10.59214731509773997054600374498201'], 'prelabel': '2-483-161.34-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9638672097745928, 'root_angle': -0.1467610279082748, 'root_number': '0.8955799111935745 - 0.4449006885435325*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0733805139541', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.65891998122955921278171525447', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.30822043262098086747536071186', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.27962647765360523109404291845', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'bad_primes': [3, 7, 23], 'central_character': '161.34', 'conductor': 483, 'conductor_radical': 483, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/483/2/r/a/34/16'], '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': '2-483-161.34-c1-0-22', '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': '2-483-161.34-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9638672097745928, 'root_angle': -0.0733805139541374, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.65891998122955921278171525447', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2102930909936253788265213426118', 'Lhash_array': ['2102930909936253788265213426118'], 'label': '2-483-161.34-c1-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/483/2/r/a/34/16'}