Table lfunc_lfunctions
L-functions
{'Lhash': '807113053802905100705428085579', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [39.560233660342064, -22.840111553002984], 'a6': [0, 0], 'a7': [245.09739920500817, -424.5211482260659], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 99.38336412377564, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '432.305', 'coefficient_field': 'CDF', 'conductor': 432, 'conductor_radical': 6, 'conjugate': '1188968440915813607052298911911', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-39.560233660342064, 22.840111553002984], [7812.5, -13531.646934131853]], [[1.0, 0], [-245.09739920500817, 424.5211482260659], [-58824.5, -101887.02272983543]], [[1.0, 0], [873.3364314848877, 504.22102381090707], [885780.5, 1534216.830353764]], [[1.0, 0], [-466.801008257647, -808.5230633266236], [-2413404.5, 4180139.2132153627]], [[1.0, 0], [0, -8090.586847068978], [-24137569.0, 0]], [[1.0, 0], [-7727.361106451927, 0], [47045881.0, 0]], [[1.0, 0], [11848.008656784516, -6840.450987355557], [74017944.5, -128202840.54581334]], [[1.0, 0], [-1964.704633813895, -1134.3227492105575], [297411660.5, 515132106.74942577]], [[1.0, 0], [-17062.56765652961, -29553.234088690715], [-443751840.5, 768600733.6982006]], [[1.0, 0], [-92058.03391134132, 0], [2565726409.0, 0]], [[1.0, 0], [-31021.55074747711, 17910.300674735547], [2375052120.5, -4113710943.3301992]], [[1.0, 0], [34570.87631485272, -59878.514239504424], [-3160681524.5, -5474460986.978255]], [[1.0, 0], [-13211.139640065476, -7627.455027493538], [5389607664.5, 9335074307.776636]], [[1.0, 0], [0, 236590.89712616897], [-22164361129.0, 0]], [[1.0, 0], [221890.42569822338, -128108.49700746992], [21090266820.5, -36529413678.29012]], [[1.0, 0], [19919.59883576767, -34501.75724993946], [-25760187180.5, -44617953009.110466]], [[1.0, 0], [-160204.27765286338, -277481.9484846307], [-45229191084.5, 78339256943.59529]], [[1.0, 0], [0, 404593.06517070974], [-128100283921.0, 0]], [[1.0, 0], [-393719.3322390539, 0], [151334226289.0, 0]], [[1.0, 0], [-449184.1270801754, 778009.730056339], [-121543727760.5, -210519911822.5058]], [[1.0, 0], [-154916.35749510274, -89441.00070167387], [163470186684.5, 283138668860.32336]], [[1.0, 0], [0, -826458.2320110666], [-496981290961.0, 0]], [[1.0, 0], [317981.1784835291, -550759.5569840999], [-416486002464.5, -721374916909.7706]], [[1.0, 0], [-227301.04476040858, -131232.31937950506], [530760075300.5, 919303417049.5492]], [[1.0, 0], [41237.992158150475, 71426.29762004355], [-597026148264.5, 1034079622241.2635]], [[1.0, 0], [0, -1036240.1965872792], [-1500730351849.0, 0]], [[1.0, 0], [-420017.9104372353, 0], [1677100110841.0, 0]], [[1.0, 0], [-1324776.275796367, 764859.9394470624], [1040975876304.5, -1803023107212.929]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 23703866, 'index': 16, 'label': '2-432-9.2-c6-0-16', 'leading_term': '2.436867017807998344225195867011911084133070769468564333', 'load_key': 'CMFs-workshop', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/432/7/q/b/305/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 24}, 'plot_values': [2.4368670178079985, 2.3509358486428082, 2.229342537831562, 2.0736201733545636, 1.8858909163609952, 1.6688325487697007, 1.4256362212896132, 1.1599558874269116, 0.8758500107655997, 0.5777162355565404, 0.270219814014865, -0.0417833130986611, -0.35332778427104256, -0.6594233363479466, -0.9551413842826673, -1.2357023847309705, -1.4965626308312943, -1.733499062871092, -1.9426906332805112, -2.1207947377272243, -2.2650172201752214, -2.37317448160857, -2.4437462724018992, -2.4759178293054656, -2.4696101314070726, -2.4254971962549905, -2.34500951779685, -2.2303229612336337, -2.0843326746515425, -1.9106118506878762, -1.7133554697528195, -1.497309474641061, -1.2676861588622994, -1.0300668908639505, -0.7902936358109464, -0.5543510672957312, -0.3282413742915917, -0.11785415450357732, 0.0711659654247468, 0.23355113890504897, 0.36453854482843223, 0.4599919905849755, 0.5165137776016073, 0.5315437936257377, 0.5034429349326905, 0.43155818244760946, 0.3162669585524046, 0.1589987739082194, -0.037767368643696, -0.27053082022704084, -0.5348228049228839, -0.825285403542545, -1.1357751308945196, -1.4594895558642107, -1.7891147358822783, -2.1169905803356386, -2.435290641004469, -2.736212271735043, -3.012172623948964, -3.256005567902122, -3.461154368841538, -3.621854817061428, -3.7333035231008256, -3.791806252219901, -3.7949014900946096, -3.7414549042040552, -3.6317209877418923, -3.4673689352430213, -3.251470686724428, -2.9884500704348262, -2.683993049227507, -2.3449202040144566, -1.9790237382273206, -1.5948724255951783, -1.2015890140722356, -0.8086056050170222, -0.4254034128795578, -0.06124404257976032, 0.2751000316777799, 0.5756077681544178, 0.8332565215477443, 1.0422456995957108, 1.1981895485043432, 1.2982721660884458, 1.3413587525697963, 1.3280582511276282, 1.2607338776623602, 1.1434595576941193, 0.9819219361967828, 0.7832693552306637, 0.5559109509738948, 0.3092707489325125, 0.053503274553695454, -0.2008213129983774, -0.4430532706208333, -0.6628101837227254, -0.8503236974286308, -0.9967746425119023, -1.0946051231698828, -1.1377965128268377, -1.1221030750438965, -1.045232079585754, -0.9069627950155664, -0.7091985712897827, -0.4559483279361901, -0.15323607273378212, 0.19106048075212922, 0.5674386321950823, 0.9650607233854859, 1.3720971118204233, 1.7761115981993354, 2.1644769893751943, 2.524807026755777, 2.8453899023150124, 3.115608074426586, 3.3263291217058057, 3.4702529546584153, 3.5422018419931462, 3.5393413799464897, 3.461322696913977, 3.3103387797884776, 3.091090751538606, 2.8106631240222604, 2.4783103845949945, 2.105160628691238, 1.703845196624732, 1.2880662839019068, 0.8721171469695274, 0.4703717062062649, 0.09676195475294205, -0.235737466407617, -0.5155979292211941, -0.7331796276848154, -0.8811107114861989, -0.9545869130616559, -0.9515785048053814, -0.8729346832843133, -0.7223792202745221, -0.5063953135042598, -0.23400186160614422, 0.08357228701896643, 0.4333053751121317, 0.8008764555213345, 1.1712177783109243, 1.5291050674456361, 1.8597629011817893, 2.149461269482301, 2.3860791804889345, 2.5596119630885132, 2.6626006614843636, 2.690464597511855, 2.641721704123029, 2.5180854877825607, 2.324432302850208, 2.0686378327268513, 1.7612870637389348, 1.4152673873482955, 1.0452595479459663, 0.667145745091022, 0.2973580923612549, -0.04780635490139003, -0.3528758165286558, -0.60387023754971, -0.7889153504370339, -0.8987773518061968, -0.9272940148220578, -0.8716819840289983, -0.7327048908858317, -0.5146925992423801, -0.22540811400310817, 0.12423479397419972, 0.5205936558718921, 0.947843205684228, 1.3886235359580485, 1.824764031116506, 2.2380527572692563, 2.611018396925773, 2.9276906266128058, 3.1743051332164303, 3.339921274627925, 3.4169236681845847, 3.4013836251369542, 3.29326216512228, 3.0964431071650975, 2.8185921594351755, 2.4708456973881545, 2.0673406833263965, 1.6246045852177724, 1.1608308513324623, 0.6950711658965588, 0.24638006468240728, -0.16704970303457162, -0.5287215838745193, -0.8246006246605712, -1.0437736109552893, -1.178971928677431, -1.226930961594916, -1.188566998544767, -1.068960816227611, -0.8771459639643592, -0.6257089029490155, -0.33021711890055006, -0.008499705474542265, 0.32018770414116954, 0.6360757710438203, 0.9198298415491062, 1.1534892947463689, 1.3213529392860832, 1.410767389237342, 1.4127792868923237, 1.3226181332896565, 1.139984090861806, 0.8691241041207107, 0.5186896361027223, 0.10137977619220456, -0.36661606053105683, -0.8663516621529882, -1.3770006387038694, -1.8768354960910192, -2.3442628930349, -2.758865344952943, -3.102398561938645, -3.359695018091037, -3.51942822472766, -3.574698375397885, -3.5234082820618684, -3.368408456757483, -3.1174013466801935, -2.782606566969216, -2.380200913160699, -1.9295583755674224, -1.4523257348797487, -0.9713780490024992, -0.5097049739667278, -0.0892830222524833, 0.27000970592832874, 0.5513812006337226, 0.7419647577804093, 0.8334657676802193, 0.8225813725784598, 0.7111694689134955, 0.5061560864050967, 0.21918348513473987, -0.13398530171174242, -0.5342769801457482, -0.9602935804108683, -1.3894235575409737, -1.7990217151748953, -2.167596979344008, -2.4759458943999046, -2.708171798514959, -2.852534906230975, -2.9020867563296533, -2.855053290202417, -2.7149436807026217, -2.4903762875175572, -2.1946280392819992], 'positive_zeros': ['0.63669993423865492256395380821616', '2.20360545667999511302458041667039', '2.80207146220647636336962681959360', '4.52199598263062352957189262162088', '5.40284236183346077254348011202415', '6.17920891250915470579592329790135', '7.57482782985247307813507164227237', '8.188364008682470806005380891230871', '9.366523215296130302426466828681305', '9.941116931743226609779079381284064'], 'prelabel': '2-432-9.2-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.969120529102637, 'root_angle': -0.04028774147675382, 'root_number': '0.9681319637494824483173107864540936082604726002006484953 - 0.2504406132530640538067728799110977616240195930359614199*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.04028774147675381', 'prec': 54}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.63669993423865492256395380822', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '2.20360545667999511302458041667', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.80207146220647636336962681959', 'prec': 100}}