-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2891523724534631362570132251300', 'a10': [0.13397459621556135, -0.2320508075688773], 'a2': [0.8660254037844386, 0.5], 'a3': [-0.5, 0.8660254037844386], 'a4': [0.5, 0.8660254037844386], 'a5': [0.0, -0.2679491924311227], 'a6': [-0.8660254037844386, 0.5], 'a7': [0.6339745962155614, -0.36602540378443865], 'a8': [0.0, 1.0], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6228331357659873, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, -0.5]]], [3, [[1.0, 0], [0.5, -0.8660254037844386]]], [13, [[1.0, 0], [-2.598076211353316, 2.5]]]], 'bad_primes': [2, 3, 13], 'central_character': '78.43', 'coefficient_field': 'CDF', 'conductor': 78, 'conductor_radical': 78, 'conjugate': '4176394615854403746723932195689', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0.2679491924311227], [-5.0, 0]], [[1.0, 0], [-0.6339745962155614, 0.36602540378443865], [3.5, -6.06217782649107]], [[1.0, 0], [4.098076211353316, 2.366025403784439], [5.5, 9.526279441628825]], [[1.0, 0], [-2.598076211353316, 2.5]], [[1.0, 0], [1.1339745962155614, 1.9641016151377546], [-8.5, 14.722431864335457]], [[1.0, 0], [1.098076211353316, -0.6339745962155614], [9.5, -16.454482671904334]], [[1.0, 0], [3.098076211353316, -5.366025403784438], [-11.5, -19.91858428704209]], [[1.0, 0], [1.2320508075688772, -2.133974596215561], [-14.5, -25.11473670974872]], [[1.0, 0], [0, -5.464101615137754], [-31.0, 0]], [[1.0, 0], [9.062177826491071, 5.232050807568878], [18.5, 32.04293994002423]], [[1.0, 0], [-9.86602540378444, -5.696152422706632], [20.5, 35.50704155516198]], [[1.0, 0], [-3.830127018922193, -6.633974596215562], [-21.5, 37.239092362730865]], [[1.0, 0], [0, 8.196152422706632], [-47.0, 0]], [[1.0, 0], [-0.4641016151377546, 0], [53.0, 0]], [[1.0, 0], [-6.928203230275509, 4.0], [29.5, -51.09549882328188]], [[1.0, 0], [0.5980762113533159, 1.0358983848622454], [-30.5, 52.827549630850754]], [[1.0, 0], [9.63397459621556, 5.56217782649107], [33.5, 58.023702053557386]], [[1.0, 0], [1.098076211353316, -0.6339745962155614], [35.5, -61.48780366869514]], [[1.0, 0], [0, 9.732050807568877], [-73.0, 0]], [[1.0, 0], [9.464101615137755, 0], [79.0, 0]], [[1.0, 0], [0, 10.196152422706632], [-83.0, 0]], [[1.0, 0], [-2.196152422706632, -1.2679491924311228], [44.5, 77.07626093681505]], [[1.0, 0], [-5.196152422706632, 3.0], [48.5, -84.00446416709055]], [[1.0, 0], [5.964101615137754, -10.330127018922193], [-50.5, -87.4685657822283]], [[1.0, 0], [-18.73205080756888, 0], [103.0, 0]], [[1.0, 0], [-0.09807621135331594, 0.16987298107780677], [-53.5, -92.66471820493493]], [[1.0, 0], [0, -5.464101615137754], [-109.0, 0]], [[1.0, 0], [-9.330127018922193, -16.160254037844386], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-78-13.4-c1-0-1', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/78/2/i/a/43/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.156194824871083, 1.1355585422414243, 1.129875795039035, 1.1361503035443479, 1.1507017195050173, 1.169434531559995, 1.188051945412865, 1.2021995104906311, 1.207558811085852, 1.1999230533696899, 1.1752814495954844, 1.1299286529478851, 1.0606053596896052, 0.9646684495284779, 0.8402834727543255, 0.6866282182941916, 0.5040929845594793, 0.29446080046204703, 0.06104922654967606, -0.1912053251225809, -0.4557393425900726, -0.72444675442004, -0.9878695116349723, -1.2355023086997237, -1.4562127252988668, -1.6387697799741676, -1.7724644823948623, -1.8477959951236234, -1.857187180662453, -1.7956844689943392, -1.6615900804198012, -1.4569706468261017, -1.1879860969661158, -0.8649870514022802, -0.502338388650755, -0.1179412094087616, 0.26755519383700216, 0.6318363976770799, 0.9522600018453414, 1.2073792000551284, 1.3785598397340935, 1.4515767923198428, 1.4180607815952473, 1.276661116232452, 1.033794995122597, 0.7038714351914966, 0.30890768522804796, -0.12250264083989802, -0.5568596827841275, -0.9579988333022598, -1.2897783372506075, -1.5190330468858706, -1.618569197223244, -1.569944966907411, -1.3657715073818557, -1.0112826690259378, -0.5249605627819744, 0.06193222289444359, 0.7069776652958409, 1.3593474883458183, 1.963522723157754, 2.4637356502457064, 2.808789262554401, 2.956840824323846, 2.879701510014398, 2.5662107122238456, 2.0242950871888095, 1.2814180650473288, 0.38325987368653663, -0.6093691784644933, -1.6252028061180142, -2.5884278472012223, -3.4253253822180345, -4.071031031878749, -4.475747977846492, -4.609759596928271, -4.46667306549436, -4.064477346338814, -3.444207038315171, -2.666248606062133, -1.8045825394117585, -0.9394955317135743, -0.14949189954424308, 0.49674269829739054, 0.9474391033055749, 1.1730856738600357, 1.1693613254218893, 0.9572625873586739, 0.5803405800088935, 0.09930399629283776, -0.4154296312587266, -0.8923812346361181, -1.2678246475913075, -1.4936790044790074, -1.5434671609201696, -1.4155382883312693, -1.13307616336829, -0.7408155479309319, -0.29881904831663847, 0.12592947915846947, 0.4690370451151532, 0.6780492143513802, 0.7203346772748189, 0.5883557905877623, 0.3014881699616964, -0.096001363299032, -0.5406853788167054, -0.9587495202474824, -1.2766775618551218, -1.4323860093306673, -1.3852075404155497, -1.1232061569767458, -0.6666141193578905, -0.06668046060076661, 0.6001479053979746, 1.2421128533367805, 1.7648702153442735, 2.0853387475724636, 2.1446969966976575, 1.918567053382421, 1.422729274036758, 0.713279177111298, -0.11910213390439565, -0.9602415929100043, -1.6875892878896768, -2.1873478299515283, -2.3712078230771025, -2.1902188837640195, -1.643629425300673, -0.7811718676474293, 0.30182670125219735, 1.476088966544439, 2.595343368461459, 3.5162962081481846, 4.118783322409463, 4.323131709066658, 4.102075310579492, 3.4853009720136585, 2.555754799168791, 1.4380652178586806, 0.280652621171173, -0.7658938976194954, -1.5709510783032787, -2.0431286248833067, -2.143659398327778, -1.8917577325910073, -1.3610105540596664, -0.6672665790203758, 0.05014982067385572, 0.6509732756436611, 1.0167015603368141, 1.069805560474117, 0.7862942575700671, 0.19952586272647552, -0.6054315831999809, -1.5060303450442523, -2.3627605822061386, -3.0425676876567334, -3.4412487794842637, -3.50103038825097, -3.220302161458732, -2.6537867268762714, -1.9030505756889018, -1.0989302524530724, -0.37887213306085615, 0.13689239431155256, 0.36616515898918145, 0.27890537611786526, -0.09788094519304524, -0.6854077423188429, -1.367641876357716, -2.012531851078605, -2.496119527974291, -2.7251541406512483, -2.6540531117215975, -2.2930487056468616, -1.7059567908144475, -0.997920859431337, -0.2953704163392404, 0.2780667556560425, 0.6251364188466002, 0.6934798915611484, 0.4854677334099867, 0.0573211767840026, -0.49245896803354305, -1.0432451368686884, -1.4771714535573433, -1.703879956644952, -1.6801419636408133, -1.4202449610177847, -0.9947484946056625, -0.517458759105058, -0.12282825047433188, 0.06200644385328933, -0.054911676265862866, -0.5082670446156674, -1.2639143967071091, -2.2207306555343886, -3.2262055184398992, -4.103380955041222, -4.684384034896191, -4.844266936548945, -4.528509068432935, -3.7684679707330346, -2.6811574582963877, -1.4526189987961522, -0.30730045635025394, 0.5313416821745547, 0.8819057301567802, 0.6400782587621106, -0.19917369207484845, -1.5368341165168808, -3.18389560752392, -4.892106473834368, -6.396053946034703, -7.458971119284899, -7.913818297303289, -7.691968666299156, -6.834102675655936, -5.481264950194375, -3.847819768239712, -2.181515805084821, -0.7183465844370452, 0.3591319367660182, 0.952098042009875, 1.0587520879784456, 0.7683951329370208, 0.23795028987152228, -0.3439214498908815, -0.7975281897884381, -0.9892333220704559, -0.8573657803425461, -0.4218522506407091, 0.2240270613608889, 0.9375420882571794, 1.5605416320340633, 1.9559625881102263, 2.038727162881551, 1.7942502944454035, 1.2805760217918238, 0.6138338643207919, -0.059549298167857936, -0.5974579985800628, -0.8955324373694391, -0.9116918159739567, -0.6759686571239464, -0.28320941571654534, 0.129875975111287, 0.4181819951786579, 0.46451962640666883, 0.2102719877877485, -0.3269965872646967, -1.0535288848094548, -1.817551085349963, -2.442024422894517, -2.764870379719057, -2.6776113783155235], 'positive_zeros': ['2.28101002280442087926870223076522', '4.41295548574965369783604137822282', '5.84002869441533288882442948255149', '7.11253044695813313555695908315437', '8.549207448099631054207377829777221', '10.27621947446913151759042079184519', '11.14920526402552747920383678637064', '12.33620932624610486368410457367073', '13.09688708779337892690664683881628', '14.13780100489033288768875557516963'], 'prelabel': '2-78-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7891977798790284, 'root_angle': -0.2479590486074333, 'root_number': '0.7116260690618662 - 0.7025584230735236*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.123979524304', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.28101002280442087926870223077', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.41295548574965369783604137822', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.84002869441533288882442948255', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.6228331357659873, 'bad_primes': [2, 3, 13], 'central_character': '13.4', 'conductor': 78, 'conductor_radical': 78, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/78/2/i/a/43/2'], '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': '2-78-13.4-c1-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-78-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7891977798790284, 'root_angle': -0.12397952430371666, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.28101002280442087926870223077', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2891523724534631362570132251300', 'Lhash_array': ['2891523724534631362570132251300'], 'label': '2-78-13.4-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/78/2/i/a/43/2'}