Table lfunc_lfunctions
L-functions
{'Lhash': '1787612225196891349206582918023', 'a10': [142030.07586809632, 246003.3076064051], 'a2': [16.0, -27.712812921102035], 'a3': [121.5, 210.4441731196186], 'a4': [-512.0, -886.8100134752651], 'a5': [-4438.43987087801, 7687.60336270016], 'a6': [7776.0, 0], 'a7': [-14427.214637615672, 42061.64786120687], 'a8': [-32768.0, 0], 'a9': [-29524.5, 51137.93406806732], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.27041358350274, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '5.5', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [-16.0, 27.712812921102035]]], [3, [[1.0, 0], [-121.5, -210.4441731196186]]], [7, [[1.0, 0], [14427.214637615672, -42061.64786120687]]]], 'bad_primes': [2, 3, 7], 'central_character': '42.37', 'coefficient_field': 'CDF', 'conductor': 42, 'conductor_radical': 42, 'conjugate': '216083657716971054813134452905', 'degree': 2, 'euler_factors': [[[1.0, 0], [-16.0, 27.712812921102035]], [[1.0, 0], [-121.5, -210.4441731196186]], [[1.0, 0], [4438.43987087801, -7687.60336270016], [-24414062.5, -42286396.66916204]], [[1.0, 0], [14427.214637615672, -42061.64786120687]], [[1.0, 0], [334697.22213651036, 579712.5938926027], [-142655835305.5, 247087154745.30405]], [[1.0, 0], [-813042.2100748197, 0], [1792160394037.0, 0]], [[1.0, 0], [4924289.189222329, 8529119.066895228], [-17135948153816.5, 29680332838276.28]], [[1.0, 0], [-6002698.953464071, 10396979.569940299], [-58245129449109.5, -100883523499283.9]], [[1.0, 0], [142537.56351261682, -246882.3019909281], [-476404878956963.5, -825157455327161.9]], [[1.0, 0], [-190583625.01493514, 0], [12200509765705828, 0]], [[1.0, 0], [95005217.178847, 164553863.1378785], [-12704238448202416, 22004386463756576]], [[1.0, 0], [84116824.89959784, -145694614.49747828], [-88958810889730200, -154081180241924220]], [[1.0, 0], [504071325.4495707, 0], [550329031716248450, 0]], [[1.0, 0], [947415745.1893989, 0], [929293739471222700, 0]], [[1.0, 0], [1176804475.4919446, -2038285142.1264915], [-1236079607542006300, -2140952682462552600]], [[1.0, 0], [2196251579.194191, 3804019321.36772], [-4634517964686095000, 8027220583427022000]], [[1.0, 0], [4594142670.649851, 7957288522.785713], [-15077944222368922000, 26115765466832577000]], [[1.0, 0], [472985471.52801013, -819234867.9284362], [-21756958805717918000, -37684158069686520000]], [[1.0, 0], [-7474043747.679278, -12945423508.973011], [-61065066452484006000, 105767797663272090000]], [[1.0, 0], [-17428097953.288517, 0], [231122292121701580000, 0]], [[1.0, 0], [2738311671.720164, 4742894942.378192], [-156863342784179860000, 271695279547292350000]], [[1.0, 0], [11199702552.955593, -19398453851.377953], [-373996905263760500000, -647781641790357200000]], [[1.0, 0], [7415304423.723172, 0], [1287831418538085800000, 0]], [[1.0, 0], [-1962763471.9633534, 3399606056.6808195], [-1387586536883495000000, -2403370381780759600000]], [[1.0, 0], [15311365669.779984, 0], [7153014030880804000000, 0]], [[1.0, 0], [41928260614.8505, 72621877657.91016], [-5578341733326583000000, 9661971304103478000000]], [[1.0, 0], [-55483214316.3214, 96099746163.10158], [-6921169353622228000000, -11987816968262345000000]], [[1.0, 0], [-44853779489.41873, 77689024987.16406], [-10524259761499174000000, -18228552618969286000000]], [[1.0, 0], [-74725476357.08604, -129428321670.25992], [-12902132026527038000000, 22347148195906435000000]], [[1.0, 0], [168872032450.86487, 0], [38358611506121120000000, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 23062816, 'index': 11, 'label': '2-42-7.2-c11-0-11', 'load_key': 'CMFs-workshop', 'motivic_weight': 11, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [11], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/42/12/e/d/37/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [0.6424255313345618, 1.0564429835836928, 1.4015809502889076, 1.6623424870267238, 1.8266009964097834, 1.8861619163728367, 1.8371706562111034, 1.6803478650032235, 1.421038734335021, 1.0690693364602273, 0.638409879446478, 0.14665208440960475, -0.38568452535802755, -0.9359950175472493, -1.4805503510393958, -1.9955410067985666, -2.4581604965324027, -2.847681720552573, -3.146476248332431, -3.3409257282518365, -3.422176098966289, -3.386689295041676, -3.2365538249419776, -2.97952492346815, -2.6287767564297475, -2.202363020452407, -1.7223976926491895, -1.213983927202161, -0.703935299895306, -0.21934878144735884, 0.2138980767125606, 0.5726432913573749, 0.837841629116239, 0.995781626437616, 1.0390339224388123, 0.9670569067120194, 0.7864019947101337, 0.5104824436089549, 0.15889558040379909, -0.24368272608484345, -0.6689822940301903, -1.086923049670344, -1.4675946609447472, -1.7833051555154016, -2.0105583658447705, -2.1318152033641335, -2.1368992716778017, -2.0239237726877826, -1.7996438256886367, -1.4791751147763417, -1.0850642184168258, -0.6457452389319066, -0.19346792941613775, 0.23816957272663505, 0.6169092256048185, 0.914538390721782, 1.1093917561483069, 1.1884308499546135, 1.1487017575817398, 0.9980097238381144, 0.7547041802174674, 0.44653611869592263, 0.10862684725258866, -0.21933301423149937, -0.4964597453867445, -0.6843689362506465, -0.7508786198274668, -0.6733948863901144, -0.44165674538877964, -0.05955162682211244, 0.45422358485514513, 1.0667922352364405, 1.733046565004387, 2.3988250730829086, 3.0051095145961195, 3.492924668653365, 3.8085382820384113, 3.9085048058998693, 3.7640822481336786, 3.364580951589859, 2.7192766862205704, 1.8576340722527926, 0.8277316875594, -0.30705489948686326, -1.4728865235426805, -2.591427264238832, -3.586433070201676, -4.390365258384683, -4.950401552372854, -5.233248165748499, -5.22824905862839, -4.948436956799071, -4.429362801260555, -3.725758352058426, -2.9063091743581366, -2.04701884071542, -1.2238071623157354, -0.505086048914947, 0.05491782642902831, 0.4213805584664984, 0.5820615116114545, 0.5480737692040523, 0.3521246473045995, 0.04438236664854792, -0.31360633675936006, -0.6562923952286024, -0.9219749783935712, -1.060231159486724, -1.0380545088421256, -0.8439600617344136, -0.48953265354048353, -0.008185013198628533, 0.5487803283230162, 1.1183831293560795, 1.633740518603382, 2.032481492268913, 2.2647703791236253, 2.2999254618613856, 2.1307624310794226, 1.7750503187715252, 1.2738126176296487, 0.6865986599575626, 0.08424221936507101, -0.46003440692766334, -0.8800680058196306, -1.1255390270435848, -1.1689197667818536, -1.009609021566945, -0.6746086466330417, -0.21552897479689997, 0.2978117928419365, 0.7864654576819949, 1.1729933227799063, 1.3922967961814385, 1.401185957481076, 1.1853417899169187, 0.7626224295039155, 0.18211317937575083, -0.4811294147303425, -1.1351074551431217, -1.6826185071707476, -2.034219023924624, -2.1207047513186175, -1.903392999925969, -1.3807209401178495, -0.5901170727401766, 0.39529191712202033, 1.4748862310567368, 2.5327334516769686, 3.45222623518552, 4.131264778662759, 4.495927894371592, 4.510713667616169, 4.183840798588622, 3.566737925606805, 2.7476295026433353, 1.8399481310753056, 0.9670495734149894, 0.24526905658546463, -0.23235094707723292, -0.4093617275724663, -0.27429757970302193, 0.1371400326231078, 0.7465453876621373, 1.443421820670679, 2.100556314038334, 2.592051347916284, 2.811482305020002, 2.6875790459190396, 2.195138672600506, 1.3595274969026985, 0.25403619944293904, -1.009615244395104, -2.296318110311416, -3.466023943850691, -4.392937759260099, -4.982654809631691, -5.184723534624878, -4.998784985326168, -4.473396087300401, -3.697748406231416, -2.787577326111887, -1.8674499156056874, -1.0521804732551405, -0.4302573916192169, -0.05184569756784934, 0.0767996829952235, -0.008296347054452521, -0.23731560158693438, -0.5205105213137065, -0.7650804465504578, -0.8921905579631804, -0.8512304354298745, -0.6288612260397857, -0.25127154979065647, 0.22078543071319812, 0.7033565130425503, 1.1051090607701908, 1.3448457854204614, 1.367594712900245, 1.156331291592574, 0.7370832301474307, 0.176275352481306, -0.42948748377763624, -0.9696517974999892, -1.3392896416386215, -1.4586490067025653, -1.2891843996098737, -0.843050414123517, -0.18406744797649188, 0.580415912209084, 1.3157669380219477, 1.8819610200389503, 2.157572549990958, 2.061797690092634, 1.5706114275892622, 0.724013500888734, -0.3772692272518607, -1.5855069957999135, -2.7282064291663373, -3.6354230799212894, -4.167713985943229, -4.240034551443462, -3.8374203007169294, -3.019561838204693, -1.9131838928748122, -0.6931804610150588, 0.44460895109535226, 1.3146101059988904, 1.7715686578217695, 1.7344012276286578, 1.1997618896797118, 0.24293072078845063, -0.9942394419094049, -2.326374220502444, -3.554782387822739, -4.4997144146576, -5.029196274615819, -5.07953593268921, -4.66404084160385, -3.8685442141821365, -2.8346547396460995, -1.733806152958788, -0.7367995381192515, 0.015693661796069316, 0.4364126116527229, 0.5044844312236515, 0.2659245421950447, -0.17820125305343382, -0.6935302841246804, -1.1398189388501865, -1.3987356767674919, -1.396710560008719, -1.118494956879834, -0.6088901591425692, 0.03759915701198945, 0.6970781826733172], 'positive_zeros': ['1.41017739815296691818861848690848', '3.68599848251949236341184665477375', '4.80076956017496878533675226296462', '6.55472289773564537949924685915797', '7.79023554992473667031767411750997', '8.641154664040193408489212265829261', '10.34185879651051346165750522504523', '12.23565027363616234892682159812244', '12.89099826640038999540420198078238', '13.87693221800644924690837174135358'], 'prelabel': '2-42-7.2-c11-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.680705377283946, 'root_angle': 0.37583589251557364, 'root_number': '-0.7108107842386724 + 0.7033832731946384*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.37583589251557364', 'prec': 57}, 'spectral_label': 'c11-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.41017739815296691818861848690848', 'prec': 110}, 'z2': {'__RealLiteral__': 0, 'data': '3.68599848251949236341184665477375', 'prec': 110}, 'z3': {'__RealLiteral__': 0, 'data': '4.80076956017496878533675226296462', 'prec': 110}}