-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2130359812335303002997695773295', 'a10': [-5.653740067067456, 29.368879311201574], 'a2': [0, -2.6750638852063147], 'a3': [0, 0], 'a4': [0.8440332100648978, 0], 'a5': [-10.978758105037366, -2.1134972134063297], 'a6': [0, 0], 'a7': [0, 15.41532090168669], 'a8': [0, -23.65835383980988], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.89577355232496, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [10.978758105037366, 2.1134972134063297]]]], 'bad_primes': [3, 5], 'central_character': '405.244', 'coefficient_field': 'CDF', 'conductor': 405, 'conductor_radical': 15, 'conjugate': '421729897760790151864902778154', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.6750638852063147], [-8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [10.978758105037366, 2.1134972134063297]], [[1.0, 0], [0, -15.41532090168669], [-343.0, 0]], [[1.0, 0], [-44.55976326503524, 0], [1331.0, 0]], [[1.0, 0], [0, 28.02331716992947], [-2197.0, 0]], [[1.0, 0], [0, 92.66145175109689], [-4913.0, 0]], [[1.0, 0], [49.581066597195175, 0], [6859.0, 0]], [[1.0, 0], [0, 0.9228087547324454], [-12167.0, 0]], [[1.0, 0], [189.84946981420242, 0], [24389.0, 0]], [[1.0, 0], [299.1801402159086, 0], [29791.0, 0]], [[1.0, 0], [0, -57.83300217412543], [-50653.0, 0]], [[1.0, 0], [287.87986727056574, 0], [68921.0, 0]], [[1.0, 0], [0, -0.5919533470031922], [-79507.0, 0]], [[1.0, 0], [0, 598.302093601997], [-103823.0, 0]], [[1.0, 0], [0, -146.33876738097086], [-148877.0, 0]], [[1.0, 0], [-193.06598188505674, 0], [205379.0, 0]], [[1.0, 0], [566.152768416024, 0], [226981.0, 0]], [[1.0, 0], [0, 355.16288201877006], [-300763.0, 0]], [[1.0, 0], [320.70290172554786, 0], [357911.0, 0]], [[1.0, 0], [0, 636.781907033463], [-389017.0, 0]], [[1.0, 0], [-287.7653830963042, 0], [493039.0, 0]], [[1.0, 0], [0, -285.05785302215406], [-571787.0, 0]], [[1.0, 0], [-331.61529681334486, 0], [704969.0, 0]], [[1.0, 0], [0, -1821.628023414445], [-912673.0, 0]], [[1.0, 0], [1147.3657439443946, 0], [1030301.0, 0]], [[1.0, 0], [0, 1582.543701136611], [-1092727.0, 0]], [[1.0, 0], [0, 385.3872998770121], [-1225043.0, 0]], [[1.0, 0], [-203.50196328595308, 0], [1295029.0, 0]], [[1.0, 0], [0, 66.01500511825469], [-1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 51, 'label': '2-405-5.4-c3-0-51', 'leading_term': '1.030096088412411851648078547896468766324449290308975769', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/405/4/b/e/244/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [1.030096088412412, 1.2485121938989756, 1.4614489675290057, 1.666264064274982, 1.8602656604954597, 2.0407161734950434, 2.2048415269125723, 2.3498471722978542, 2.472941792002412, 2.5713692734865, 2.642449173001082, 2.6836254902490304, 2.6925231676683, 2.6670113204258303, 2.605271807447607, 2.505871380725097, 2.3678353103459964, 2.1907200867599212, 1.9746825603529394, 1.7205427021975719, 1.4298370695129168, 1.1048600451425568, 0.7486900015676251, 0.3651977244565614, -0.040965275812133134, -0.46440053100832646, -0.8990199103530698, -1.338127271758624, -1.7745245770332807, -2.200641776999746, -2.6086889070815182, -2.9908279294127964, -3.3393609426983124, -3.6469304886198635, -3.9067268493718585, -4.112696492688383, -4.25974521688837, -4.343929116460946, -4.362626263343713, -4.314682010680742, -4.200521098606186, -4.02222029161153, -3.783536110857369, -3.489883337978646, -3.148261343139464, -2.7671269003963817, -2.356213956250202, -1.926302758837091, -1.4889427706374947, -1.0561358025358836, -0.6399877400776666, -0.2523389981043604, 0.09561464903631302, 0.393698041599075, 0.6331158348803027, 0.8067810711019919, 0.9095995229293133, 0.9386970281746383, 0.8935784293475549, 0.7762086866724484, 0.5910092092172957, 0.34476537966423976, 0.04644454212427084, -0.2930727363047083, -0.6613416667328821, -1.0447724262864524, -1.4291060455776412, -1.7999304647711734, -2.1432177103214296, -2.4458613031263288, -2.696191970988725, -2.884449603753213, -3.003190223060387, -3.0476085641395985, -3.015759662985283, -2.9086665395003823, -2.7303055487330044, -2.4874660754755262, -2.18948676851107, -1.8478762120503522, -1.475831551275445, -1.0876738511616912, -0.6982235974806216, -0.32214348445175356, 0.026721758703698837, 0.3359774617541796, 0.5952521557053719, 0.7966825875084336, 0.935284654276891, 1.0091889730033887, 1.019725757174404, 0.9713506776778081, 0.871411137323991, 0.7297605243797282, 0.5582361274199705, 0.37002406555816464, 0.1789413875163431, -0.001328985430357409, -0.15801091426933664, -0.2799737843108796, -0.3583960082710788, -0.38731438579288496, -0.36402505835386656, -0.2893085258527732, -0.16745974176923692, -0.006114301692857335, 0.1841272921262964, 0.3902639278218536, 0.5976222008138095, 0.7907138649709406, 0.9541786474200556, 1.0737618057265494, 1.1372714818994993, 1.1354594853639708, 1.0627708474801134, 0.9179123977208661, 0.7041986008539285, 0.4296436666414575, 0.106782023397129, -0.24778599993792477, -0.6141107767664047, -0.9698440527536303, -1.2913806100153575, -1.5551347602216323, -1.7388850197560053, -1.823113190277081, -1.7922608720713469, -1.6358275560858704, -1.349240019195678, -0.9344326757096829, -0.40009244293807017, 0.2384610680555047, 0.9597694815646471, 1.7370919652405197, 2.5395907331327376, 3.333792117959763, 4.085251403540518, 4.760334865376831, 5.328022194681547, 5.761627486885996, 6.040337786280631, 6.150474993008742, 6.086399601140923, 5.850992728876803, 5.455675358880709, 4.91994945357054, 4.270473220971821, 3.53971068158547, 2.764222143154169, 1.9826855643014722, 1.233757538808091, 0.5538954433293175, -0.02473183741868232, -0.4761188703124611, -0.7819679655842514, -0.9328032276432522, -0.9285781782315858, -0.7787295271001926, -0.501662189703004, -0.12368503080869238, 0.32254904350621033, 0.8000132629575489, 1.269574748958611, 1.6924261576504276, 2.032534335535862, 2.2589548094142247, 2.3478660320314217, 2.2841917440216983, 2.0627029230771234, 1.6885213239566261, 1.176982801164575, 0.5528582645019273, -0.15102922723597534, -0.8957136846719792, -1.638409307500941, -2.3351067831830834, -2.943282277544842, -3.424548894415592, -3.7470815299372515, -3.887658232249903, -3.83318381879531, -3.5815933083183604, -3.1420717550997366, -2.534570861578501, -1.788648449619331, -0.941701457096799, -0.036703574837433146, 0.8804078502814389, 1.76352682745814, 2.5691737423423597, 3.2591075497928075, 3.802583767218241, 4.178110131223104, 4.374585331841821, 4.391747907582965, 4.239909364717549, 3.938994649764977, 3.5169608302857203, 3.007707843286297, 2.4486303557321154, 1.8779845648960767, 1.3322562752397646, 0.8437158108780767, 0.4383311958652891, 0.13418446799500994, -0.05950118194659323, -0.1426608970964682, -0.1240015708739064, -0.019967400805545554, 0.14685603705679823, 0.3497709940372982, 0.560269579767119, 0.7504279888041719, 0.895205842405189, 0.9744714546910763, 0.9745955927151586, 0.8894903874991478, 0.721013950659649, 0.4787116433958792, 0.17891795946795816, -0.15670551662533663, -0.5030747171087969, -0.8338723221545354, -1.1238394469254684, -1.3509778625821116, -1.4984765503144222, -1.5561973695763571, -1.521589425351969, -1.3999477661868487, -1.2039857982221627, -0.9527480268389542, -0.6699458297146694, -0.3818493048600234, -0.11490856760399978, 0.10669535075326764, 0.2633591452128279, 0.34202120369834704, 0.33760055209158185, 0.25377000181251835, 0.10297513508109724, -0.09432797461519218, -0.3111781214469931, -0.516255197611886, -0.6765076655926734, -0.7600557664696715, -0.7391347637789524, -0.592830974556108, -0.3093719545223636, 0.11223911687730177, 0.6614078190649497, 1.316052628927442, 2.0436574821555693, 2.8032244006780695, 3.548002301443515, 4.228800328477451, 4.797639839823158, 5.2114633986628185], 'positive_zeros': ['1.68055757000529195869479657161953', '3.63598085636196034220391261460002', '4.36946036278885485483575446100234', '5.90060029210838188348025619730804', '6.81976471063727728192260424332559', '7.38522395929396702602217737131609', '8.318548311475368850399573836176403', '9.185861532411412571817194660401256', '10.68416717340197256066558379746364', '11.20003447905153756847293938049476'], 'prelabel': '2-405-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.8883303440259604, 'root_angle': -0.9394634093399697, 'root_number': '-0.98196997725561316099169402475448619718007872420033803893 - 0.1890369375773173365624953166529045512157652402924785529*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.46973170466998493', 'prec': 67}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.68055757000529195869479657162', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.63598085636196034220391261460', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.36946036278885485483575446100', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 23.89577355232496, 'bad_primes': [3, 5], 'central_character': '5.4', 'conductor': 405, 'conductor_radical': 15, 'degree': 2, 'index': 51, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/405/4/b/e/244/5'], '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': '2-405-5.4-c3-0-51', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-405-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.8883303440259604, 'root_angle': -0.4697317046699849, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.68055757000529195869479657162', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2130359812335303002997695773295', 'Lhash_array': ['2130359812335303002997695773295'], 'label': '2-405-5.4-c3-0-51', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/405/4/b/e/244/5'}