-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1477306454715397763603430202624', 'a10': [2.9409209390434734, 1.1623183859406399], 'a2': [-1.1584559306791384, -0.8111595753452777], 'a3': [0.0, 0.0], 'a4': [0.6840402866513374, 1.8793852415718169], 'a5': [-2.1748764959244955, 0.5195307762541006], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.7320508075688773, -2.732050807568877], 'a9': [-1.0260604299770062, 2.8190778623577253], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.908929749574751, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.1584559306791384, 0.8111595753452777]]], [5, [[1.0, 0], [2.1748764959244955, -0.5195307762541006]]], [37, [[1.0, 0], [-5.296135581389781, 2.991813480739921]]]], 'bad_primes': [2, 5, 37], 'central_character': '740.287', 'coefficient_field': 'CDF', 'conductor': 740, 'conductor_radical': 370, 'conjugate': '552529683644935887393611582823', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.1584559306791384, 0.8111595753452777]], [[1.0, 0], [0, 0], [1.0260604299770062, -2.8190778623577253]], [[1.0, 0], [2.1748764959244955, -0.5195307762541006]], [[1.0, 0], [0, 0], [6.893654271085456, -1.2155372436685123]], [[1.0, 0], [0, 0], [5.5, -9.526279441628825]], [[1.0, 0], [4.909122688321199, 2.2891615043866294], [8.35623892592501, 9.958577760546714]], [[1.0, 0], [-7.0648922416070565, 3.294413356301205], [10.927389364671168, -13.022755533022627]], [[1.0, 0], [0, 0], [17.854159794932258, 6.498382723187706]], [[1.0, 0], [0, 0], [-19.91858428704209, 11.5]], [[1.0, 0], [4.014422817278205, 6.953184282589642], [-14.5, 25.11473670974872]], [[1.0, 0], [0, 0], [31.0, 0]], [[1.0, 0], [-5.296135581389781, 2.991813480739921]], [[1.0, 0], [-11.798998218694171, 4.2944841457646215], [31.4078221678781, -26.354291997148113]], [[1.0, 0], [0, 0], [0, -43.0]], [[1.0, 0], [0, 0], [-40.703193977868615, 23.5]], [[1.0, 0], [-1.268834024063768, 14.502839258572013], [-52.194810909647025, -9.203353416347309]], [[1.0, 0], [0, 0], [-10.24524248234889, 58.10365742772028]], [[1.0, 0], [1.8102047071465648, 4.973496557475654], [-46.728711030257664, 39.2100441908789]], [[1.0, 0], [0, 0], [65.98211945181794, -11.634427903684333]], [[1.0, 0], [0, 0], [66.71817607579949, 24.28343017612248]], [[1.0, 0], [7.026279441628825, -7.026279441628825], [0, -73.0]], [[1.0, 0], [0, 0], [-13.718206035687498, -77.79981248796443]], [[1.0, 0], [0, 0], [-53.35137160398276, 63.581688778875176]], [[1.0, 0], [-2.010221135763013, 1.686775813603517], [15.4546878123568, -87.64789001808651]], [[1.0, 0], [3.845427517117506, 14.351330870705972], [-84.00446416709055, 48.5]], [[1.0, 0], [4.359894054042596, -7.551558017219224], [-50.5, -87.4685657822283]], [[1.0, 0], [0, 0], [89.20061658979718, 51.5]], [[1.0, 0], [0, 0], [-68.77827423645971, -81.96675541373065]], [[1.0, 0], [1.9907310488960823, 11.289996805352846], [-102.42649566566402, 37.28019562249789]], [[1.0, 0], [-10.942851769252757, 15.628011942332746], [-38.64827619580057, -106.18526614880764]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 57, 'label': '2-740-740.287-c1-0-57', '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/740/2/ce/b/287/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.5598817712918561, 0.6710839368878723, 0.7604502841221448, 0.823614626030121, 0.8528912160919178, 0.8379339128400937, 0.7669692046614667, 0.6284134140002733, 0.41271392045082333, 0.11427475421800086, -0.2666839379614486, -0.7225151724334493, -1.2369984505399967, -1.784886997170836, -2.332362263568288, -2.8385542613775576, -3.25819190364054, -3.5453182730108708, -3.6578527689806832, -3.562622721137615, -3.240343609013009, -2.689924542845681, -1.9314385922600705, -1.0071457295074424, 0.019899479798101877, 1.069884470387871, 2.052832157607305, 2.8773024037890877, 3.4603921035810616, 3.737919966669526, 3.673489753687518, 3.265094328565535, 2.54808395325256, 1.5936816871631019, 0.50276129595961, -0.6047488995693263, -1.6037949745129154, -2.3798140035079505, -2.843970125243441, -2.945791761156217, -2.68117351460977, -2.094230786968031, -1.2723159230077452, -0.3345183890464918, 0.584971543822397, 1.356331094460596, 1.8734799917120817, 2.070258335755547, 1.9306405458805056, 1.4910597360698, 0.8341569019508505, 0.07471916005003355, -0.6600158048071606, -1.2523994615190017, -1.6148859582621082, -1.7052508325540907, -1.533563044825499, -1.159386270096248, -0.6794910547294691, -0.20821500922762998, 0.14585172147496978, 0.3022855490907205, 0.22576366986472488, -0.0661568938600915, -0.5063535718502552, -0.9922445773909285, -1.408076947698453, -1.650894313948983, -1.654644202594987, -1.4069854890719868, -0.9546561531170272, -0.39556064810338565, 0.14140115795730387, 0.5249119102364744, 0.6522104494517318, 0.47549798451222125, 0.017376089372571644, -0.6290192465664123, -1.3163129343643758, -1.8730337852455416, -2.1416354232404577, -2.0161642911834043, -1.4708216343200744, -0.5721388875176069, 0.5292360565453736, 1.6266880491788047, 2.5005853130180014, 2.967074690141746, 2.921763566004626, 2.367758730654559, 1.4204684520468733, 0.2865067128046137, -0.7800563948653814, -1.5353080118890725, -1.8043341550758896, -1.52754011958549, -0.7827654252244163, 0.22352977923828957, 1.1958707034585372, 1.8127913006543896, 1.7999867561523908, 0.9972081823096832, -0.5968744093656624, -2.813240358762557, -5.338640098402193, -7.774820282415796, -9.718536580539821, -10.844802651651424, -10.974582988045618, -10.11133370990027, -8.437796995572707, -6.273667399776068, -4.003976053263656, -1.9950140381393053, -0.5175703390736278, 0.30461099517001655, 0.5095481063605153, 0.27249990398021473, -0.1504228577383592, -0.4952653454645846, -0.5606796094602063, -0.25770785577190464, 0.37341611244679324, 1.1827527577304506, 1.959914020637061, 2.4985897722481085, 2.6578717551570117, 2.4030571979195487, 1.8145971730857364, 1.0630231318595884, 0.3574779090102265, -0.11688225486055076, -0.25407131494791035, -0.058586626085925804, 0.3566788069483552, 0.8056316979288396, 1.087093856229389, 1.048601445572836, 0.6366013852681291, -0.08256297982222663, -0.9380261010731593, -1.7024481700341914, -2.159027774693808, -2.1676078837432997, -1.7096884797048946, -0.8979786707446005, 0.053486928048254445, 0.8906889519884273, 1.3945281331088835, 1.4466439404972449, 1.0655578641431114, 0.4010647401883087, -0.3126117462568229, -0.8314454058804172, -0.9812878152846346, -0.7173210383426767, -0.14328040592767702, 0.5177148270891256, 0.9938625778272719, 1.056388335382758, 0.6037954543758144, -0.28924260615331193, -1.3768563306235284, -2.3035489863693863, -2.7074652554065537, -2.336363314942772, -1.141281696234377, 0.6827166007544515, 2.7253125249230634, 4.455902623211617, 5.361444714528588, 5.089770588891168, 3.5573535464324344, 0.9889309273670936, -2.125223760074709, -5.145340388187873, -7.44114608871102, -8.550469150806167, -8.293524822872962, -6.81120281263407, -4.517317989992486, -1.9794806176063868, 0.23636855868011755, 1.7127651087190157, 2.277374062655334, 2.0238441075589533, 1.2545267812848129, 0.36629110948677723, -0.28278487130788343, -0.48358812330862966, -0.22959242238830202, 0.30031321762357704, 0.8207716634756289, 1.0518444819942123, 0.8249901521514634, 0.1472173710312634, -0.7977382779569056, -1.7107682957728232, -2.279638800998815, -2.2867913673801032, -1.6857030515852758, -0.6197140940898218, 0.6230402171398776, 1.7031285832401826, 2.3398100606666525, 2.4000754091289167, 1.9367004551977527, 1.162997482007306, 0.3738949677342105, -0.15848426478023855, -0.27792163129264946, 0.0066498097755101305, 0.5324891547012114, 1.049975307940999, 1.3201087213757405, 1.2064977977891438, 0.7276701144559778, 0.04996458528650468, -0.5768754096980261, -0.9178172834791855, -0.847576046049883, -0.4059324373991968, 0.2094830738251297, 0.7129189568002584, 0.8390059093995592, 0.4504549253808315, -0.39639352522669397, -1.455912212537929, -2.3705011814650194, -2.7967832776985877, -2.5367958057792808, -1.6255340334019925, -0.3390379075539284, 0.8860700047039526, 1.5990252172111232, 1.4993388422971459, 0.5614838142435222, -0.9275148123610584, -2.43718908325286, -3.3528216009925833, -3.17580177460498, -1.6993598653265147, 0.90095689031474, 4.096441193999611, 7.1493444539389115, 9.328525645155368, 10.128097850225894, 9.418092678273288, 7.477712916892001, 4.900333389047159, 2.4020391174850273, 0.597557824977142, -0.18215905546605998, 0.0286010212641093, 0.8739626365041536, 1.8262508408049545, 2.3868695287074564], 'positive_zeros': ['1.16538930715563236393422809885623', '2.99763707570021274780286869493783', '4.30612666802313543436407907615399', '5.41924098150301787805046440912640', '6.38718058077528971102940477932474', '7.44123510612343512073777996626257', '7.85244896606736890829881276353975', '8.964724818684473679895287205519308', '9.503770865255050967996005272417791', '10.44140534360214979312985743932075'], 'prelabel': '2-740-740.287-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.430829025162969, 'root_angle': 0.5596665629533362, 'root_number': '-0.18635224310935364 + 0.9824829980656725*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.279833281477', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.16538930715563236393422809886', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.99763707570021274780286869494', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.30612666802313543436407907615', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.908929749574751, 'bad_primes': [2, 5, 37], 'central_character': '740.287', 'conductor': 740, 'conductor_radical': 370, 'degree': 2, 'index': 57, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/740/2/ce/b/287/1'], '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': '2-740-740.287-c1-0-57', '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': '2-740-740.287-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.430829025162969, 'root_angle': 0.2798332814766681, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.16538930715563236393422809886', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1477306454715397763603430202624', 'Lhash_array': ['1477306454715397763603430202624'], 'label': '2-740-740.287-c1-0-57', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/740/2/ce/b/287/1'}