Table lfunc_lfunctions
L-functions
{'Lhash': '1035224008167175064755401640529', 'a10': [0, 0], 'a2': [0, -1024.0], 'a3': [0, 12234.542831936957], 'a4': [-1048576.0, 0], 'a5': [0, 0], 'a6': [12528171.859903444, 0], 'a7': [0, -906115293.7796264], 'a8': [0, 1073741824.0], 'a9': [10310669164.6935, 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': '1158214164605622989760688033723', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1024.0]], [[1.0, 0], [0, -12234.542831936957], [-10460353203.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 906115293.7796264], [-558545864083284030, 0]], [[1.0, 0], [-87557511113.63313, 0], [7400249944258161000000, 0]], [[1.0, 0], [0, -37829873122.5831], [-247064529073450400000000, 0]], [[1.0, 0], [0, 10319718874384.64], [-69091933913008730000000000, 0]], [[1.0, 0], [-44734681374964.57, 0], [714209495693373300000000000, 0]], [[1.0, 0], [0, -293023555555994.56], [-39471584120695487000000000000, 0]], [[1.0, 0], [-456583541974000.2, 0], [5132842708382183000000000000000, 0]], [[1.0, 0], [-5317391395265199.0, 0], [20825506393391553000000000000000, 0]], [[1.0, 0], [0, -23362370744687130], [-855531895666462800000000000000000, 0]], [[1.0, 0], [75434059364417400, 0], [7386879101213258000000000000000000, 0]], [[1.0, 0], [0, -159217806186091400], [-20083415214428110000000000000000000, 0]], [[1.0, 0], [0, 5361266218215294.0], [-130033429462229770000000000000000000, 0]], [[1.0, 0], [0, -1470563096127942000], [-1621038246414955000000000000000000000, 0]], [[1.0, 0], [-2787529009350196000, 0], [15413179794770735000000000000000000000, 0]], [[1.0, 0], [5950479951885501000, 0], [31040344686800427000000000000000000000, 0]], [[1.0, 0], [0, 3150765368883513000], [-222623423334106740000000000000000000000, 0]], [[1.0, 0], [-36068560406155903000, 0], [752359350923790900000000000000000000000, 0]], [[1.0, 0], [0, -51683969389605750000], [-1348279907365869100000000000000000000000, 0]], [[1.0, 0], [-121307627448549520000, 0], [7082211906170644000000000000000000000000, 0]], [[1.0, 0], [0, -100530858103924620000], [-19982045332214680000000000000000000000000, 0]], [[1.0, 0], [272642167111087260000, 0], [86534669543385680000000000000000000000000, 0]], [[1.0, 0], [0, -506239838293624000000], [-527480512638944850000000000000000000000000, 0]], [[1.0, 0], [-486404712830295400000, 0], [1232391940347446500000000000000000000000000, 0]], [[1.0, 0], [0, -1488316225694288300000], [-1860294571709496000000000000000000000000000, 0]], [[1.0, 0], [0, 2486762129545690600000], [-4140562374860212000000000000000000000000000, 0]], [[1.0, 0], [-2290138621554071000000, 0], [6108807736878339000000000000000000000000000, 0]], [[1.0, 0], [0, 3868847404089286000000], [-13021089174137413000000000000000000000000000, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 23221663, 'index': 19, 'label': '2-50-5.4-c21-0-19', 'leading_term': '2.884794412828131076077696966662415161762595297157996142', '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/49/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 20}, 'plot_values': [2.884794412828131, 2.911715414951618, 2.8785304776880825, 2.7840456537831706, 2.6288885977956906, 2.415518203269943, 2.1481798656075175, 1.8328072355797098, 1.4768729043294215, 1.0891919739104872, 0.6796838739646902, 0.2590990439612809, -0.16128182553445505, -0.5699674418044238, -0.9555852837811726, -1.307211182638687, -1.6146895120573839, -1.868934589759687, -2.0622043645324317, -2.188338197786548, -2.2429515264719755, -2.223581388486013, -2.129778169794429, -1.9631404559978962, -1.7272914971939293, -1.4277974775550988, -1.0720294718736902, -0.6689726215275407, -0.22898762371638298, 0.23646894569874058, 0.7151577065228583, 1.1943941431629488, 1.6614012800016875, 2.1036672624546586, 2.5092975210654167, 2.8673512742011624, 3.1681525039894844, 3.403566212078048, 3.567231709936032, 3.654745897782181, 3.6637909041657273, 3.5942020552455807, 3.4479738736260197, 3.229203621386922, 2.9439737477229255, 2.6001764237801344, 2.2072850912155166, 1.7760795636517444, 1.3183326516969665, 0.846467487412866, 0.3731956640729194, -0.0888530497831826, -0.5274983396529328, -0.9313632455474415, -1.2902036088656745, -1.5952030190760118, -1.8392242058949912, -2.0170091024671764, -2.125321336586264, -2.1630266461233196, -2.1311086102945644, -2.032619083293282, -1.8725647502036764, -1.6577332338936703, -1.3964641023699615, -1.0983718972097647, -0.7740298671846486, -0.43462439467647906, -0.0915911009255445, 0.24375572654517608, 0.5605884506407519, 0.8489143029817837, 1.099895136325459, 1.306128192944541, 1.4618785720907588, 1.5632555990548702, 1.6083270908686342, 1.5971675246769526, 1.5318382813581506, 1.4163003898987672, 1.2562624639803723, 1.05896872601454, 0.8329340808831254, 0.587635060422681, 0.3331670443107118, 0.0798794154367011, -0.16199881993399085, -0.3827299609999068, -0.5734220872496412, -0.7263545068081605, -0.8352624769396632, -0.8955707849541895, -0.9045674489950012, -0.8615108001991721, -0.7676654771534724, -0.626265326378867, -0.4424037763737128, -0.22285484942060568, 0.024169495978420205, 0.28931762910222275, 0.5624419300974084, 0.8329759064640075, 1.090331355740809, 1.3243012408432773, 1.5254534968472258, 1.6855010658135414, 1.7976340681359675, 1.8568011545431962, 1.8599287128919784, 1.806068680299877, 1.6964681687151801, 1.5345568700028156, 1.3258511713981749, 1.0777769802113102, 0.7994163180177987, 0.5011856867471756, 0.19445692104586648, -0.10886638239774743, -0.396801823057952, -0.6577540758923754, -0.8809763739707797, -1.0570100505869964, -1.178085020266969, -1.2384651509571645, -1.234724178379199, -1.1659400902828427, -1.0337986924547453, -0.842600268291322, -0.5991667499203995, -0.3126505072140151, 0.005750402650779563, 0.3431620377853663, 0.6854775259801816, 1.0178582239484446, 1.3252755789720922, 1.5930742353625846, 1.807535662753195, 1.9564210730535652, 2.0294726763074933, 2.0188534117642343, 1.919507157765797, 1.729424020597993, 1.4497985468941885, 1.0850724880936438, 0.6428579367914877, 0.1337411023643811, -0.42902846801128725, -1.0299539597109097, -1.6517991876778293, -2.276171078102592, -2.8841562958802007, -3.4569890999936086, -3.9767258607755718, -4.426900938672116, -4.793138852935227, -5.0636988731994865, -5.2299303215951305, -5.286619914240296, -5.232216298376774, -5.068921421274494, -4.80264333649477, -4.44281032607348, -4.002051591184475, -3.4957550277457496, -2.941517545761652, -2.358507808666919, -1.7667649748893923, -1.1864598562225859, -0.6371467361408303, -0.13703482352035024, 0.29769209646854, 0.6534808164662242, 0.9199143397096006, 1.0900973554314513, 1.1609054973349795, 1.1330876168381383, 1.0112161042415768, 0.803486373038259, 0.5213727394954937, 0.1791538294215417, -0.20667392110131694, -0.6180713673545121, -1.0361932256697846, -1.4421562264578311, -1.8178074275245586, -2.1464610212811968, -2.4135730507299216, -2.607325828844432, -2.7190974522001587, -2.7437964770144827, -2.680047399961921, -2.53021883125744, -2.3002929046946674, -1.9995812574059373, -1.6402995393617592, -1.2370185893146999, -0.8060158649873672, -0.36455519285025545, 0.06987380259128602, 0.480323279355802, 0.8511279551012902, 1.1685862547840276, 1.4215514563763287, 1.60190629252832, 1.7048995208029212, 1.7293290443068914, 1.677562989107895, 1.5553974272588265, 1.3717568513050755, 1.138250723012207, 0.8686061043339931, 0.5780022195724297, 0.2823375147830414, -0.002536858955457163, -0.2615813820566288, -0.4812943741657368, -0.6503656026593093, -0.7602259257283441, -0.8054662138203108, -0.7841047159639599, -0.6976890153725881, -0.5512264399711769, -0.3529449058227722, -0.11389429771972875, 0.152593753224863, 0.43156282452897304, 0.7071745995476286, 0.9635023880510423, 1.185337053760035, 1.3589660324356978, 1.472886905319902, 1.5184196501468712, 1.4901861303648456, 1.3864314197623788, 1.209168930807806, 0.9641396873459355, 0.6605850673436747, 0.31084151305325564, -0.07022537955183757, -0.46592176330527085, -0.8585287016979589, -1.2301692362607786, -1.563697172164555, -1.8435635725201927, -2.0566172707202273, -2.192798197360064, -2.2456868949691198, -2.2128800764666376, -2.096170190424153, -1.9015163199928882, -1.638803924693169, -1.3214014469973543, -0.9655321335018195, -0.5894890460365508, -0.21272966732507492, 0.14510670663704664, 0.46521082304421973], 'positive_zeros': ['0.816647748189281839926973140227741', '2.00370898954655685192423903305801', '3.57219287206846856339653282093423', '4.80019834530534787569066858793327', '5.99927986966738806376465771220314', '6.88400869378908868044409306098153', '8.201059230233311228849501625222902', '9.139399784424586789883114110421317', '10.21257277718661739502692596469055', '11.90376220522992904895281027965562'], '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': '0.816647748189281839926973140228', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.00370898954655685192423903306', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.57219287206846856339653282093', 'prec': 100}}