Table lfunc_lfunctions
L-functions
{'Lhash': '1500494760622449769269735528880', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-3.414213562373095, 0.0], 'a6': [0.0, 0.0], 'a7': [0.585786437626905, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.795065251406015, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '4608.1', 'coefficient_field': 'CDF', 'conductor': 4608, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.414213562373095, 0], [5.0, 0]], [[1.0, 0], [-0.585786437626905, 0], [7.0, 0]], [[1.0, 0], [2.0, 0], [11.0, 0]], [[1.0, 0], [2.8284271247461903, 0], [13.0, 0]], [[1.0, 0], [-7.656854249492381, 0], [17.0, 0]], [[1.0, 0], [-5.656854249492381, 0], [19.0, 0]], [[1.0, 0], [6.82842712474619, 0], [23.0, 0]], [[1.0, 0], [3.414213562373095, 0], [29.0, 0]], [[1.0, 0], [-7.414213562373095, 0], [31.0, 0]], [[1.0, 0], [-1.6568542494923801, 0], [37.0, 0]], [[1.0, 0], [-0.3431457505076198, 0], [41.0, 0]], [[1.0, 0], [9.65685424949238, 0], [43.0, 0]], [[1.0, 0], [-4.48528137423857, 0], [47.0, 0]], [[1.0, 0], [-7.899494936611665, 0], [53.0, 0]], [[1.0, 0], [-4.0, 0], [59.0, 0]], [[1.0, 0], [-1.6568542494923801, 0], [61.0, 0]], [[1.0, 0], [8.0, 0], [67.0, 0]], [[1.0, 0], [14.82842712474619, 0], [71.0, 0]], [[1.0, 0], [-9.65685424949238, 0], [73.0, 0]], [[1.0, 0], [-14.242640687119286, 0], [79.0, 0]], [[1.0, 0], [-13.313708498984761, 0], [83.0, 0]], [[1.0, 0], [2.0, 0], [89.0, 0]], [[1.0, 0], [9.313708498984761, 0], [97.0, 0]], [[1.0, 0], [13.556349186104045, 0], [101.0, 0]], [[1.0, 0], [5.0710678118654755, 0], [103.0, 0]], [[1.0, 0], [7.31370849898476, 0], [107.0, 0]], [[1.0, 0], [18.82842712474619, 0], [109.0, 0]], [[1.0, 0], [6.0, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 20156596, 'index': 44, 'label': '2-4608-1.1-c1-0-44', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/4608/2/a/e/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 17}, 'plot_values': [-1.300512958459262e-61, 0.1402524039289985, 0.27953388520245814, 0.4168410729893153, 0.5511079324669514, 0.6811798607816522, 0.8057938879654478, 0.9235663914006993, 1.0329892923841473, 1.1324352505579063, 1.2201719421389716, 1.2943851255885503, 1.3532098761382985, 1.3947691104506297, 1.4172183192368035, 1.4187952695768644, 1.3978733198341153, 1.353016899667427, 1.2830376395697858, 1.1870495854696588, 1.0645219038990243, 0.9153274739745121, 0.7397857773891501, 0.5386985409835436, 0.313376662576082, 0.06565706344239558, -0.20209173690530532, -0.4869763344812896, -0.7855982190218488, -1.0940871175661626, -1.408148092656447, -1.7231222408544122, -2.034060468593053, -2.3358094368467284, -2.623108373431403, -2.8906950628808987, -3.1334189506647028, -3.346358953512595, -3.524943263528367, -3.665068183182139, -3.7632128431426017, -3.816546546173415, -3.8230254573992197, -3.781475431635813, -3.691657937317844, -3.5543163062751733, -3.3711999086184825, -3.145064318465232, -2.879646091958692, -2.579611413384503, -2.2504785642200535, -1.898514916582838, -1.53060992689217, -1.1541263853847155, -0.7767329383946461, -0.40622161786470085, -0.05031476086990119, 0.2835337440497902, 0.5883375109565071, 0.8577713416928324, 1.0863537342352232, 1.2696124398667819, 1.404227510261652, 1.4881466771291338, 1.5206684930536885, 1.5024894246491025, 1.4357120137694632, 1.3238122885852852, 1.1715657870833027, 0.9849328186981957, 0.7709048982811973, 0.5373155996149316, 0.2926203497526266, 0.04565087589951473, -0.19464892109061907, -0.4194980009004449, -0.6205557782180848, -0.7901934925225438, -0.9217504024236418, -1.0097659795176055, -1.0501797046213057, -1.040490799996212, -0.979871254836665, -0.8692267970932465, -0.7112020011248761, -0.5101274560243925, -0.2719088027886338, -0.0038594209320847797, 0.2855194584149511, 0.5868054846948876, 0.8899612023768159, 1.1846701367644221, 1.4606923465065678, 1.7082277599094906, 1.918274902247542, 2.0829723216947236, 2.1959101612383156, 2.2523999172432982, 2.2496914704626327, 2.1871279537484383, 2.0662308971586123, 1.8907103138539119, 1.666396892215467, 1.4010961606466117, 1.1043673002168846, 0.787232097268435, 0.4618222492997944, 0.1409757579453552, -0.16220463915585392, -0.43481622506372103, -0.6646281363645253, -0.8405433693862236, -0.9530338670572248, -0.9945320337056519, -0.9597631020076405, -0.846004472694779, -0.6532604215900398, -0.3843433541803315, -0.044855997013263336, 0.3569275603274883, 0.8102803434782678, 1.3023350927178383, 1.818481903891647, 2.3428383853282257, 2.8587767356625378, 3.3494895859239042, 3.7985745120370846, 4.190615906677292, 4.511742472558615, 4.750139003971373, 4.8964923691262365, 4.944353668626865, 4.890401367560385, 4.734593690152592, 4.480202606596559, 4.133726185334204, 3.7046807635400296, 3.205279121759905, 2.65000544568886, 2.05510212878237, 1.4379872312867241, 0.8166244973540617, 0.20887009817989932, -0.3681783986497336, -0.8988050138561151, -1.3692452072581536, -1.7681792855866691, -2.0871288358653017, -2.3207393374366023, -2.4669365644815846, -2.5269494547018323, -2.5051975891494584, -2.409047080710228, -2.2484442683193313, -2.0354419203835117, -1.783637430052872, -1.5075465194150963, -1.2219390683401699, -0.9411656911455583, -0.6785044884754601, -0.4455569403992731, -0.2517201711312572, -0.10375985307445329, -0.005503930455315203, 0.04232771471683173, 0.04214835771191646, -0.0006186556742340614, -0.07780750941557646, -0.17891178322974816, -0.29160408304940433, -0.4023512953918779, -0.49709856685615306, -0.5619914675016023, -0.5841034601337857, -0.5521349023550838, -0.4570504285672659, -0.2926237019435605, -0.055862129655833204, 0.25271093181783494, 0.6289328848168209, 1.0650469607270034, 1.5499175587213312, 2.069409961807212, 2.6069208380591578, 3.1440386869529435, 3.6613069398303453, 4.139057085433461, 4.5582752380911025, 4.901463211896439, 5.1534545544482455, 5.302147196241492, 5.339117371693272, 5.26008416609336, 5.065200258927393, 4.7591519123599495, 4.351059673537625, 3.8541802486518932, 3.2854191580676937, 2.6646726711382924, 2.0140257252860017, 1.3568396580803328, 0.7167692672306569, 0.1167526656725103, -0.42198060300876583, -0.8808378120576807, -1.2446844963108377, -1.5025201983723562, -1.6479757853333274, -1.6796074083642751, -1.6009712784614805, -1.4204734210701373, -1.150998990407806, -0.8093360818024096, -0.4154187815872221, 0.008577039085559351, 0.43924438480182804, 0.8530159990964515, 1.2272458651243485, 1.541250794272788, 1.7772629807038876, 1.9212482056862663, 1.9635504095683194, 1.8993313495015955, 1.728783664840487, 1.4571064319979246, 1.094243694642447, 0.6543979516354635, 0.15534160881964104, -0.3824405989808801, -0.936736740959909, -1.4846724067996995, -2.003802858128385, -2.4731788465196645, -2.8743333790496375, -3.1921404110831415, -3.415502639653881, -3.5378339769076366, -3.557312502642493, -3.476891231011901, -3.3040663075785264, -3.050414661276381, -2.730925037984613, -2.3631571214728657, -1.9662725351803216, -1.5599884250760427, -1.1635086654678335, -0.7944892488125493, -0.46809300254413094, -0.19618445676172633, 0.013291346026044934, 0.15671172195690408, 0.2349378543670791, 0.2532245808970392, 0.22088148612748426, 0.15070171820347064, 0.05818763766473226, -0.03938628681152509], 'positive_zeros': ['1.18368165514401114435917186045649', '2.63184720196125191377722589765154', '3.43062905228760822552862115730600', '4.07877026859228326780039657759834', '5.03696118046026676399820726801012', '5.53684307330550041869603099292582', '6.67286284599277986422052759465507', '7.64426205909419015540685432305335', '7.78077750188482996790771674327288'], 'prelabel': '2-4608-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.065893606996912, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.18368165514401114435917186046', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.63184720196125191377722589765', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.43062905228760822552862115731', 'prec': 100}}