Table lfunc_lfunctions
L-functions
{'Lhash': '824147147659463409372928421090', 'a10': [0, 0], 'a2': [0, -1024.0], 'a3': [0, 185808.3290627499], 'a4': [-1048576.0, 0], 'a5': [0, 0], 'a6': [190267728.9602559, 0], 'a7': [0, -488078923.6006628], 'a8': [0, 1073741824.0], 'a9': [-24064381946.09114, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 139.73867214353106, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '10.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1024.0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '50.49', 'coefficient_field': 'CDF', 'conductor': 50, 'conductor_radical': 10, 'conjugate': '64416737081066194755865022745', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1024.0]], [[1.0, 0], [0, -185808.3290627499], [-10460353203.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 488078923.6006628], [-558545864083284030, 0]], [[1.0, 0], [72857788192.6602, 0], [7400249944258161000000, 0]], [[1.0, 0], [0, -902767943297.1908], [-247064529073450400000000, 0]], [[1.0, 0], [0, -6320654824580.124], [-69091933913008730000000000, 0]], [[1.0, 0], [43678011741764.914, 0], [714209495693373300000000000, 0]], [[1.0, 0], [0, 90068215776475.38], [-39471584120695487000000000000, 0]], [[1.0, 0], [-1348539975369753.0, 0], [5132842708382183000000000000000, 0]], [[1.0, 0], [456363129576530.1, 0], [20825506393391553000000000000000, 0]], [[1.0, 0], [0, -28493149552884892], [-855531895666462800000000000000000, 0]], [[1.0, 0], [142955129398543120, 0], [7386879101213258000000000000000000, 0]], [[1.0, 0], [0, -147393206495939140], [-20083415214428110000000000000000000, 0]], [[1.0, 0], [0, 171829627982635040], [-130033429462229770000000000000000000, 0]], [[1.0, 0], [0, -1364816119500064500], [-1621038246414955000000000000000000000, 0]], [[1.0, 0], [6604551498728514000, 0], [15413179794770735000000000000000000000, 0]], [[1.0, 0], [-1481712484222757400, 0], [31040344686800427000000000000000000000, 0]], [[1.0, 0], [0, 28003644440376250000], [-222623423334106740000000000000000000000, 0]], [[1.0, 0], [43188247569832665000, 0], [752359350923790900000000000000000000000, 0]], [[1.0, 0], [0, -289648060609041540], [-1348279907365869100000000000000000000000, 0]], [[1.0, 0], [-52262482510112200000, 0], [7082211906170644000000000000000000000000, 0]], [[1.0, 0], [0, 59180927608712600000], [-19982045332214680000000000000000000000000, 0]], [[1.0, 0], [-479550444577965900000, 0], [86534669543385680000000000000000000000000, 0]], [[1.0, 0], [0, 816242262916330300000], [-527480512638944850000000000000000000000000, 0]], [[1.0, 0], [-455684251566156000000, 0], [1232391940347446500000000000000000000000000, 0]], [[1.0, 0], [0, -1933448953070168800000], [-1860294571709496000000000000000000000000000, 0]], [[1.0, 0], [0, -754692062974832700000], [-4140562374860212000000000000000000000000000, 0]], [[1.0, 0], [-889717504577546400000, 0], [6108807736878339000000000000000000000000000, 0]], [[1.0, 0], [0, 4930070706899307000000], [-13021089174137413000000000000000000000000000, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 23221658, 'index': 15, 'label': '2-50-5.4-c21-0-15', 'leading_term': '0.175685564812038826080419136010013504487797255491443397', 'load_key': 'CMFs-workshop', 'motivic_weight': 21, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [21], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/50/22/b/h/49/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.07421875', 'prec': 24}, 'plot_values': [0.1756855648120388, 0.38620702584351374, 0.5374330007661194, 0.6261718560641737, 0.6514298659315418, 0.6144337113966395, 0.518578402268462, 0.3693021458490056, 0.17389209340637002, -0.058772816028515654, -0.3185335990618322, -0.5943074081357136, -0.8744764845592922, -1.1472970786044245, -1.4013147997153426, -1.6257725653059794, -1.8109974708821555, -1.9487535053210248, -2.032548066780897, -2.057881666738028, -2.022431998852195, -1.9261656407628776, -1.7713729853722733, -1.5626244903531166, -1.3066489112592017, -1.012136761959628, -0.6894747425184694, -0.3504192072187043, -0.007718836699997859, 0.32530154241024717, 0.6351826407250509, 0.9087835593334217, 1.1337309568600558, 1.2988496330398491, 1.3945600795112296, 1.4132294767761255, 1.3494640000538012, 1.2003320961552946, 0.9655105544546967, 0.6473476508503133, 0.25084031697633274, -0.2164749077462367, -0.7447145375317572, -1.3219190184501866, -1.9343937804163152, -2.567110010261152, -3.2041526037919184, -3.829201059745177, -4.4260278400505415, -4.978997986620966, -5.473553586534808, -5.896667028970963, -6.237247894225492, -6.486489734627224, -6.638144908080078, -6.688717949085975, -6.637570635786936, -6.486934847916957, -6.241832412170777, -5.909904293610981, -5.5011546056915295, -5.027617868423432, -4.502960638886939, -3.9420309727904, -3.3603710631086257, -2.773709769250027, -2.197452542047991, -1.6461864299330284, -1.1332174048509436, -0.6701561799272142, -0.2665670339956305, 0.07030803782009838, 0.3357401915417653, 0.5276130044210126, 0.6464268446953115, 0.6952085048337224, 0.6793297579442852, 0.6062418930847807, 0.4851364538412716, 0.3265452239872817, 0.1418948631877362, -0.05696660155167705, -0.25825305381648667, -0.4507144794335191, -0.6240834536396921, -0.7694762644629256, -0.8797326690219798, -0.9496805810292568, -0.9763148573976325, -0.9588826883301933, -0.8988717770646273, -0.7999013848091219, -0.6675202643230796, -0.5089193572676023, -0.33257073119804254, -0.14780743339597954, 0.03563839566969525, 0.20811979501602412, 0.36056102575108057, 0.4849243227549112, 0.574636704093229, 0.624957454027051, 0.6332689894867182, 0.5992766756149914, 0.5251066758357152, 0.4152949786950165, 0.276665184986001, 0.11809729208365907, -0.049805607783438774, -0.21514128446441755, -0.36520739337531544, -0.4870563569382401, -0.5680839777650102, -0.5966275824864419, -0.5625483725550493, -0.45777256152518786, -0.2767668403370499, -0.01692572315039716, 0.32114866741916276, 0.7334899119048967, 1.212744572149181, 1.748289050359129, 2.3264860016470594, 2.9310744691140775, 3.5436821832003025, 4.144443057653256, 4.712698058545664, 5.227753539388103, 5.669668017444246, 6.020036371643787, 6.262739685879192, 6.384629508765809, 6.376117164578118, 6.231641886991756, 5.949995859094878, 5.534489578775537, 4.992947129120042, 4.337527679278129, 3.584376601236085, 2.7531166702131133, 1.8661966203617348, 0.9481205565687939, 0.024587097929030115, -0.8784286008973047, -1.735613846102039, -2.5232408256575587, -3.220034938503429, -3.8079531895652035, -4.2728400407120475, -4.604932791731428, -4.7991945272928165, -4.855459671870264, -4.77838495939806, -4.5772068226511635, -4.265314486997954, -3.8596560508081184, -3.380002191512881, -2.8480985140539317, -2.286742655806701, -1.7188258288110656, -1.1663803299025808, -0.6496745695968508, -0.18639532962335198, 0.20904669069407364, 0.5260573012008776, 0.7582212617526697, 0.903470726654193, 0.9640524536159604, 0.9462957405421994, 0.8601922672984936, 0.7188078165847808, 0.5375538110216643, 0.33335334646256115, 0.12374158828153903, -0.0740562410871785, -0.24402470646826355, -0.372192019111726, -0.4473569588845187, -0.4616727741535511, -0.41105863971225537, -0.295417425337154, -0.11864783526820165, 0.11155101117954581, 0.38407425133007966, 0.6849869299461006, 0.9982531513525504, 1.306583277574096, 1.5923573801947815, 1.838578798098445, 2.0298095288043094, 2.1530394318490917, 2.1984438775480726, 2.159989443327022, 2.035854335195048, 1.8286390768262595, 1.5453532500430334, 1.1971751976748057, 0.7989930677397596, 0.3687468134155914, -0.07339880671063595, -0.5060111028466425, -0.9074298320108113, -1.2568397017322854, -1.535321148103164, -1.7268257706736267, -1.8190257850104474, -1.803992473842983, -1.6786666388252311, -1.4450941075995232, -1.1104109531987234, -0.6865756631054682, -0.1898584195646816, 0.35988974342848956, 0.9401535186062253, 1.5268112332218962, 2.09528181694074, 2.6217033015995668, 3.0840829903804567, 3.463360197347498, 3.7443263319251248, 3.9163539349130487, 3.9738957512396853, 3.916726591213312, 3.74991400233547, 3.4835179665503206, 3.1320342092506457, 2.7136094885770254, 2.249069675505637, 1.7608118436618068, 1.2716193660098731, 0.8034636978763121, 0.3763578057094301, 0.007323951539925651, -0.2904671724190187, -0.5083378918326683, -0.6424892169769939, -0.6941082461209893, -0.6691901548555313, -0.5780835770002217, -0.43478388824742636, -0.2560134784522758, -0.06014070707092886, 0.1340008646327226, 0.3083247890945724, 0.4466645906095286, 0.5358373180799869, 0.5665331032962277, 0.5339749874360746, 0.43830559542398756, 0.2846722930318528, 0.08299945939234388, -0.1525454757981738, -0.40436754832207666, -0.6524996244659402, -0.875840892560031, -1.053509647303585, -1.166233087969488], 'positive_zeros': ['0.65013746493795918596145825288597', '2.07980996568353320145676973922148', '3.00988520159584953203531880765252', '5.25268897648368828027180591454082', '5.99073796817444288330856780288498', '7.11035132011884550545396479556212', '7.993736184524541857816320411120145', '8.687759748702197804934877019418619', '10.54105184001769903769579446173657', '12.05671047064175990649041102492101'], 'prelabel': '2-50-5.4-c21-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.821111290548409, 'root_angle': 0.17620819117478337, 'root_number': '0.4472135954999579392818347337462552470881236719223051449 + 0.89442719099991587856366946749251049417624734384461028971*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.17620819117478337', 'prec': 57}, 'spectral_label': 'c21-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.65013746493795918596145825289', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '2.07980996568353320145676973922', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.00988520159584953203531880765', 'prec': 100}}