Table lfunc_lfunctions
L-functions
{'Lhash': '897497202833974232181253037414', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-8.288736943359885, -8.288736943359885], 'a4': [0.0, 0.0], 'a5': [-10.288736943359885, 22.784685473149317], 'a6': [0.0, 0.0], 'a7': [3.2072115864295454, -3.2072115864295454], 'a8': [0.0, 0.0], 'a9': [0.0, 56.406320232437956], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.269597046707549, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [10.288736943359885, -22.784685473149317]]]], 'bad_primes': [2, 5], 'central_character': '80.33', 'coefficient_field': 'CDF', 'conductor': 80, 'conductor_radical': 10, 'conjugate': '1700801480596422557176324633606', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [8.288736943359885, 8.288736943359885], [0, 81.0]], [[1.0, 0], [10.288736943359885, -22.784685473149317]], [[1.0, 0], [-3.2072115864295454, 3.2072115864295454], [0, -2401.0]], [[1.0, 0], [-19.569370946298633, 0], [14641.0, 0]], [[1.0, 0], [-219.84005834328576, -219.84005834328576], [0, 28561.0]], [[1.0, 0], [-281.35221275391746, 281.35221275391746], [0, -83521.0]], [[1.0, 0], [0, -305.64770492488697], [-130321.0, 0]], [[1.0, 0], [-633.2432283579795, -633.2432283579795], [0, 279841.0]], [[1.0, 0], [0, -885.2097835302593], [-707281.0, 0]], [[1.0, 0], [1383.3205292705322, 0], [923521.0, 0]], [[1.0, 0], [-453.9869854974997, 453.9869854974997], [0, -1874161.0]], [[1.0, 0], [193.00279441037063, 0], [2825761.0, 0]], [[1.0, 0], [-1016.6649948914021, -1016.6649948914021], [0, 3418801.0]], [[1.0, 0], [-1203.5253090584774, 1203.5253090584774], [0, -4879681.0]], [[1.0, 0], [530.1744440173713, 530.1744440173713], [0, 7890481.0]], [[1.0, 0], [0, 934.8008335298417], [-12117361.0, 0]], [[1.0, 0], [1122.317652538966, 0], [13845841.0, 0]], [[1.0, 0], [4760.404659898396, -4760.404659898396], [0, -20151121.0]], [[1.0, 0], [-8831.100033746516, 0], [25411681.0, 0]], [[1.0, 0], [-3008.633647497312, -3008.633647497312], [0, 28398241.0]], [[1.0, 0], [0, 3349.0879757968037], [-38950081.0, 0]], [[1.0, 0], [-3166.084888182176, -3166.084888182176], [0, 47458321.0]], [[1.0, 0], [0, -1732.325113573375], [-62742241.0, 0]], [[1.0, 0], [-1659.4257225716947, 1659.4257225716947], [0, -88529281.0]], [[1.0, 0], [8976.873892305484, 0], [104060401.0, 0]], [[1.0, 0], [-3702.137662886997, -3702.137662886997], [0, 112550881.0]], [[1.0, 0], [-11888.651600084482, 11888.651600084482], [0, -131079601.0]], [[1.0, 0], [0, 6698.680729316571], [-141158161.0, 0]], [[1.0, 0], [7366.507299944827, 7366.507299944827], [0, 163047361.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 10801978, 'index': 2, 'label': '2-80-5.3-c4-0-2', 'load_key': 'CMFs-workshop', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/80/5/p/g/33/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [1.0629550528492788, 0.9509017972969054, 0.8047052183582434, 0.6255551324991634, 0.4149291391326288, 0.17470525150872007, -0.09270770518466333, -0.3842337637969001, -0.6960006614747004, -1.0232316684657636, -1.3601722932771712, -1.7000651882518, -2.0351852894259763, -2.3569451404295303, -2.656077404801224, -2.9228977263815334, -3.1476463704724917, -3.320901565240017, -3.434051356656924, -3.479804391595555, -3.4527137595511577, -3.3496823551888872, -3.1704137419235905, -2.9177698031648003, -2.5979961474150834, -2.220778795233242, -1.7991014899024333, -1.3488822053683966, -0.8883799777421701, -0.4373786542972918, -0.01617179455318692, 0.35560830573240937, 0.6602560453632894, 0.8832744286626708, 1.0145825716868573, 1.0495503829379165, 0.989761392714202, 0.8434122310737711, 0.6252735759117101, 0.3561624793378665, 0.06190898647284526, -0.22816083567732523, -0.48316052085935296, -0.6728894337415176, -0.7702420557257901, -0.7536010041006146, -0.6090144575703511, -0.33195391988444134, 0.07153869102432792, 0.5844736219837109, 1.179414068955687, 1.8198972277056331, 2.462739512679391, 3.0611060937675636, 3.568143014187383, 3.940898376029047, 4.14420568698961, 4.154174889291136, 3.960940540675182, 3.5703552181492197, 3.0043893611348373, 2.300102718810916, 1.5071798891832129, 0.6841623798700351, -0.10635112192834577, -0.803140699983157, -1.3519479075805514, -1.7106647009665261, -1.8535894287736452, -1.7742691007284135, -1.4865614392186788, -1.0237128021265205, -0.43544519020905215, 0.2167417919251543, 0.865642543569878, 1.44520446463162, 1.8974668161528394, 2.1788221630124105, 2.264876370548866, 2.1533019693797066, 1.8642767201195107, 1.4383569621717438, 0.9319275654463802, 0.4106643910764243, -0.05829442193792707, -0.41457953979573164, -0.6122390658926454, -0.6258390983302513, -0.4541907118461185, -0.12112975166693936, 0.3268846186847681, 0.8261966195647329, 1.3038557302652674, 1.6870960098061276, 1.9132420475805594, 1.9387714574813377, 1.7463028475169984, 1.3484807711785745, 0.7880791760497952, 0.13410534705721294, -0.5257970674702764, -1.095840318474287, -1.4842457957063002, -1.6155363364101218, -1.4413467520893914, -0.9482461680108196, -0.16139048006420775, 0.8566742532527997, 2.012115571190355, 3.1902233430347997, 4.268911515114945, 5.133629443933916, 5.691739504855705, 5.884416683129433, 5.694396672255258, 5.148416155107564, 4.3138900057537075, 3.2901627223852623, 2.1954449658402226, 1.1511873173631704, 0.26605286324723565, -0.37824192896538444, -0.737170602889856, -0.8082089210753217, -0.6294747482371523, -0.2723635600652784, 0.17074165940209546, 0.6018341939447885, 0.933357957892145, 1.1024695021817568, 1.0811945379120942, 0.8807842232963063, 0.5494631107599978, 0.16380593868941862, -0.18497640345032193, -0.40768809387318955, -0.4340275789687795, -0.2268509975495174, 0.20869789933049174, 0.8229561449348808, 1.5270983760695416, 2.2055384504269275, 2.7336359340950236, 2.998007972690966, 2.9161935137220336, 2.45237891644851, 1.6264004377592778, 0.5142291649955963, -0.7605266625573616, -2.043105931692085, -3.169715525870004, -3.991921882795841, -4.39945328299217, -4.337683844382003, -3.816827496874859, -2.9111488761004356, -1.74810018977728, -0.4889579874987909, 0.6960196674970591, 1.6539205205459917, 2.272673320161041, 2.4978000823199893, 2.3395981178233973, 1.8695162207164617, 1.2063255096100973, 0.49445096608910605, -0.12178724286460434, -0.5235263656200702, -0.637847291314516, -0.4497646411241039, -0.0035847805848843567, 0.6066019413508438, 1.255553848420559, 1.8112063652728132, 2.160181299099363, 2.229692677993782, 2.0016807889280432, 1.5164136055065283, 0.8647497681064326, 0.17040576623636083, -0.43448881012604423, -0.8359037905251634, -0.9613400952514072, -0.7955039319456749, -0.38493342140382486, 0.1696503190205006, 0.7321342521159805, 1.1575990388972661, 1.3217173537558962, 1.1472643019259594, 0.6224058006314639, -0.19315232573813215, -1.1758442801814184, -2.1588104216621513, -2.961867303189418, -3.42545002531538, -3.442134883301999, -2.9795978611286897, -2.0903105607815897, -0.9056756075112546, 0.3847799674057171, 1.565655296182018, 2.4335916146464585, 2.8338543721190086, 2.6886869535492184, 2.01198295138607, 0.907350478249446, -0.4502188549520336, -1.8457169560442164, -3.0626287704113953, -3.921280664484491, -4.3097352271733325, -4.201390716585329, -3.656062337024921, -2.804597675943521, -1.8203558978825887, -0.8834942442258449, -0.14541550412615722, 0.29936520206732803, 0.4282720215433035, 0.28975625519871445, -0.013066121080330615, -0.3504109016935107, -0.5991295639985609, -0.6738224812437407, -0.5487013585260343, -0.26512174134606536, 0.07716881668520335, 0.3434067776250643, 0.39682342657496283, 0.13398982821714883, -0.4855666770459337, -1.4225403811561927, -2.5582970169911063, -3.7134105617651927, -4.681132560996642, -5.269219459801063, -5.341436124546462, -4.849760206731792, -3.849954299743328, -2.4964561625479624, -1.0168017308991788, 0.32985089775522086, 1.302022670931848, 1.7230871919724802, 1.5165586447563524, 0.722013072417521, -0.5119209944297513, -1.9563184211784794, -3.3467031428417044, -4.434619038775539, -5.035372699213157, -5.062074365197524, -4.5390101712519915, -3.5918033231101267, -2.4168119512214488, -1.2366775164702077], 'positive_zeros': ['0.70800045586093495469549639117442', '3.75507096491613724091460507026311', '5.02609073427527949881214730963751', '5.98026619304886231120817763353670', '7.982504911922789007839600245380446', '9.084025684758939263771169993963200', '10.48302554546263533703964024020833', '11.16139124394418453712286023705688', '12.39992135910893438460990091715371', '13.27156380018041605529213663067267'], 'prelabel': '2-80-5.3-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8756907077617977, 'root_angle': -0.09438977163714926, 'root_number': '0.8292296172349617 - 0.5589080800099056*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0943897716371', 'prec': 40}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.70800045586093495469549639117', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '3.75507096491613724091460507026', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '5.02609073427527949881214730964', 'prec': 100}}