-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1401264743354365969598206524727', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-2.8284271247461903, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 76.46474497557813, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '9576.1', 'coefficient_field': 'CDF', 'conductor': 9576, 'conductor_radical': 798, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.8284271247461903, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [2.0, 0], [11.0, 0]], [[1.0, 0], [-4.82842712474619, 0], [13.0, 0]], [[1.0, 0], [4.0, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.8284271247461901, 0], [23.0, 0]], [[1.0, 0], [-7.656854249492381, 0], [29.0, 0]], [[1.0, 0], [-1.17157287525381, 0], [31.0, 0]], [[1.0, 0], [8.82842712474619, 0], [37.0, 0]], [[1.0, 0], [2.0, 0], [41.0, 0]], [[1.0, 0], [-1.6568542494923801, 0], [43.0, 0]], [[1.0, 0], [10.48528137423857, 0], [47.0, 0]], [[1.0, 0], [6.0, 0], [53.0, 0]], [[1.0, 0], [4.0, 0], [59.0, 0]], [[1.0, 0], [6.0, 0], [61.0, 0]], [[1.0, 0], [-11.313708498984761, 0], [67.0, 0]], [[1.0, 0], [13.65685424949238, 0], [71.0, 0]], [[1.0, 0], [-10.0, 0], [73.0, 0]], [[1.0, 0], [-14.82842712474619, 0], [79.0, 0]], [[1.0, 0], [-15.65685424949238, 0], [83.0, 0]], [[1.0, 0], [-11.65685424949238, 0], [89.0, 0]], [[1.0, 0], [11.65685424949238, 0], [97.0, 0]], [[1.0, 0], [-12.48528137423857, 0], [101.0, 0]], [[1.0, 0], [-2.8284271247461903, 0], [103.0, 0]], [[1.0, 0], [-2.34314575050762, 0], [107.0, 0]], [[1.0, 0], [-12.142135623730951, 0], [109.0, 0]], [[1.0, 0], [-2.0, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 87, 'label': '2-9576-1.1-c1-0-87', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/9576/2/a/bl/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-7.730151790468137e-61, 0.17405593541778952, 0.34634526425040685, 0.5150677160666566, 0.678359272487139, 0.8342689737131515, 0.9807454214487697, 1.1156351008399468, 1.2366938551285898, 1.3416120251411594, 1.4280529745028083, 1.4937040066736298, 1.53633806878997, 1.5538841403983503, 1.5445038208789652, 1.5066713491784154, 1.4392541027029548, 1.341590519277975, 1.2135623603041874, 1.0556582814078672, 0.8690257987211887, 0.6555089360953319, 0.4176691133616954, 0.15878718993418367, -0.11715498840230416, -0.4055146813285247, -0.7010505449322632, -0.9980070393068936, -1.290220178944086, -1.571243128871619, -1.8344894145479465, -2.073390789648762, -2.2815661180139406, -2.452997000428404, -2.5822053402304177, -2.6644276199712436, -2.6957803787527403, -2.67341125786435, -2.5956300384162705, -2.4620143413519613, -2.273485104173468, -2.0323475899367964, -1.742294515366218, -1.4083688915393613, -1.0368853301332701, -0.635309850924993, -0.21209959547862994, 0.22349473491734992, 0.6616594894714123, 1.0922761436699748, 1.5052000101718752, 1.8905516661565622, 2.239012300156231, 2.5421135589531976, 2.792512148082386, 2.9842394389751927, 3.112916682708726, 3.1759271337924373, 3.1725374435665827, 3.1039620740063563, 2.973366177434403, 2.7858043405518527, 2.5480947441718205, 2.2686305735485317, 1.9571328493172835, 1.6243511500090835, 1.2817208742102704, 0.9409876534929281, 0.6138111890860847, 0.3113620654805772, 0.0439259227696934, -0.17947030957570956, -0.3513956406957799, -0.46630202342730437, -0.5207488080358242, -0.513554211492585, -0.44586575562912667, -0.3211444345164277, -0.14506050766872083, 0.07469782841097465, 0.3286981865305948, 0.6061120371027217, 0.8951257097365761, 1.1834000854467799, 1.4585622551816877, 1.7087105325347236, 1.9229129979690884, 2.0916792989882382, 2.2073857879285845, 2.2646352674491537, 2.2605346203541266, 2.1948763769452944, 2.07021373662839, 1.8918225949222829, 1.6675485866212079, 1.4075418701167635, 1.123887157674571, 0.8301411413864354, 0.5407937711205653, 0.2706736112901048, 0.034320554489936976, -0.15464865781003517, -0.2841554926526863, -0.3442285788133837, -0.32750094906587457, -0.22961218032757125, -0.04949534332761438, 0.21046703963032673, 0.5444287099377458, 0.9432119821494924, 1.3945853989982022, 1.883679160694654, 2.393524555720737, 2.90569781882805, 3.401043712119837, 3.860449918543074, 4.265640273213318, 4.599953112532164, 4.849070716498081, 5.001667017387307, 5.049943443312787, 4.990026884759296, 4.822209175029953, 4.551013956900106, 4.185084106380555, 3.736890692607275, 3.2222724289919995, 2.65982235438112, 2.0701457108163464, 1.4750193075386768, 0.8964877612815939, 0.3559356100955683, -0.12682379691918566, -0.5344016636640407, -0.8525902163848821, -1.0709868060855277, -1.1834555782234852, -1.188403570289239, -1.0888562554733678, -0.8923265836123809, -0.6104810711716157, -0.25861601856793437, 0.14503396930849902, 0.5801247614906059, 1.0251314499142195, 1.4583344659914024, 1.858817135905469, 2.20742757384826, 2.48765889922192, 2.6864051055259073, 2.7945553899754443, 2.8073971497095607, 2.7248068378720323, 2.5512180387445245, 2.2953669843504625, 1.969826767750285, 1.5903521615570448, 1.1750666809036574, 0.7435318287534664, 0.31574487913783794, -0.08888427326287164, -0.4525249987827851, -0.7598353241350422, -0.9987412115364962, -1.1610442300282187, -1.2428244920554397, -1.2446159564097217, -1.1713427938348966, -1.0320178991798168, -0.8392171844915818, -0.6083553482492001, -0.35679974482341376, -0.10286817740135286, 0.13523661378346688, 0.3404987124237133, 0.49810864549670064, 0.5963742172183688, 0.6274707169547568, 0.5879863305959645, 0.4792287759399012, 0.3072714060291463, 0.08273067165175974, -0.1797187935105903, -0.46207085838006534, -0.7439221998820487, -1.003568077871098, -1.2192036535350106, -1.370167949142225, -1.4381638085646673, -1.4083869906826367, -1.2705009015924267, -1.019400343782956, -0.6557177366188212, -0.18603806768929823, 0.3771962648163826, 1.0160933242377317, 1.7080181106753634, 2.4265672244389567, 3.142766305813631, 3.8264319897164327, 4.447630153397204, 4.978155763326129, 5.3929570646143326, 5.6714284179506, 5.798501768376791, 5.7654762941787645, 5.570538781361756, 5.218943050351257, 4.7228345114746695, 4.100724705102509, 3.3766394773861967, 2.5789822203160866, 1.7391693702896227, 0.8901082118226753, 0.06459621837893825, -0.7062738818089939, -1.3946187359787867, -1.9770983732502714, -2.436008002350119, -2.760068798271102, -2.9448750422724284, -2.9929736663938615, -2.9135724405269494, -2.721893607030492, -2.4382095569240603, -2.0866150225204905, -1.6936051965380985, -1.2865402938591775, -0.8920836731676114, -0.5347023054769777, -0.2353149672830271, -0.01016519147121224, 0.13001683927485425, 0.18051592515739476, 0.14276900533306808, 0.024131129032007086, -0.16271463418567766, -0.40066712586419767, -0.6693815437511961, -0.9466370983130389, -1.2098147173592755, -1.437394635692143, -1.6103820379510563, -1.7135727442308044, -1.7365800737723809, -1.6745580060282437, -1.5285737984630734, -1.3056042802724686, -1.018152888519298, -0.6835077906441069, -0.3226837421063227, 0.040889704385767445, 0.3828546341274803, 0.6794950837045808, 0.9092941081472226, 1.0543799882432465, 1.1017694565325096], 'positive_zeros': ['1.10540297389681392526699458540717', '2.17917649493817097690997598026177', '3.28973185598106911419952532301906', '3.68809063160133001641568423848066', '4.69512817192142540259275188360700', '4.97886634915747501555036272942501', '6.17452172159072746067291518206162', '6.63994601206952979782139814487608', '7.48935662020286926813297623600302'], 'prelabel': '2-9576-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.744412214413163, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.10540297389681392526699458541', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.17917649493817097690997598026', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.28973185598106911419952532302', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 76.46474497557813, 'bad_primes': [2, 3, 7, 19], 'central_character': '1.1', 'conductor': 9576, 'conductor_radical': 798, 'degree': 2, 'index': 87, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9576/2/a/bl/1/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-9576-1.1-c1-0-87', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-9576-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.744412214413163, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.10540297389681392526699458541', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1401264743354365969598206524727', 'Lhash_array': ['1401264743354365969598206524727'], 'label': '2-9576-1.1-c1-0-87', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9576/2/a/bl/1/1'}