-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '5621858480604906257651892621037', 'a10': [13.104686356149273, 13.790627287701454], 'a2': [0.0, -1.7015621187164243], 'a3': [0.0, -3.0], 'a4': [5.104686356149273, 0.0], 'a5': [-8.104686356149273, 7.701562118716424], 'a6': [-5.104686356149273, 0.0], 'a7': [0.0, 22.209372712298546], 'a8': [0.0, -22.298437881283576], 'a9': [-9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8850286500861096, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 3.0]]], [5, [[1.0, 0], [8.104686356149273, -7.701562118716424]]]], 'bad_primes': [3, 5], 'central_character': '15.4', 'coefficient_field': 'CDF', 'conductor': 15, 'conductor_radical': 15, 'conjugate': '3541126538220584193284780025771', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.7015621187164243], [-8.0, 0]], [[1.0, 0], [0, 3.0]], [[1.0, 0], [8.104686356149273, -7.701562118716424]], [[1.0, 0], [0, -22.209372712298546], [-343.0, 0]], [[1.0, 0], [1.790627287701454, 0], [1331.0, 0]], [[1.0, 0], [0, 58.209372712298546], [-2197.0, 0]], [[1.0, 0], [0, -18.984378812835757], [-4913.0, 0]], [[1.0, 0], [104.83749084919418, 0], [6859.0, 0]], [[1.0, 0], [0, -49.612496949731394], [-12167.0, 0]], [[1.0, 0], [-293.4656089860898, 0], [24389.0, 0]], [[1.0, 0], [-64.41874542459709, 0], [29791.0, 0]], [[1.0, 0], [0, 19.884354410686914], [-50653.0, 0]], [[1.0, 0], [165.5812545754029, 0], [68921.0, 0]], [[1.0, 0], [0, -247.34996339677673], [-79507.0, 0]], [[1.0, 0], [0, -384.54371492191103], [-103823.0, 0]], [[1.0, 0], [0, 463.5280937347468], [-148877.0, 0]], [[1.0, 0], [-73.79062728770145, 0], [205379.0, 0]], [[1.0, 0], [137.34996339677673, 0], [226981.0, 0]], [[1.0, 0], [0, -173.90627287701454], [-300763.0, 0]], [[1.0, 0], [594.2811813689564, 0], [357911.0, 0]], [[1.0, 0], [0, 320.2312911786262], [-389017.0, 0]], [[1.0, 0], [-770.4686356149273, 0], [493039.0, 0]], [[1.0, 0], [0, 173.92492069301628], [-571787.0, 0]], [[1.0, 0], [1019.0249450951651, 0], [704969.0, 0]], [[1.0, 0], [0, -384.3749084919418], [-912673.0, 0]], [[1.0, 0], [-34.49055408125493, 0], [1030301.0, 0]], [[1.0, 0], [0, -1756.303099835284], [-1092727.0, 0]], [[1.0, 0], [0, 1361.7374664470453], [-1225043.0, 0]], [[1.0, 0], [321.11867221815055, 0], [1295029.0, 0]], [[1.0, 0], [0, -1582.246668344302], [-1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-15-5.4-c3-0-2', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/15/4/b/a/4/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [1.02312657344382, 1.058421374821203, 1.1019645697968146, 1.1541634373267933, 1.2149950026525123, 1.283989934542759, 1.3602136172265489, 1.442243022193148, 1.5281408071025149, 1.6154311013150076, 1.701083942554411, 1.7815169582905732, 1.8526235920180405, 1.9098370219401652, 1.9482379497934978, 1.9627126322262458, 1.9481648286922195, 1.8997816974134816, 1.8133490885437331, 1.6856062606148745, 1.5146240077305593, 1.3001838997054018, 1.0441303222562877, 0.7506619112206756, 0.4265255576062677, 0.08107522070085707, -0.2738399028275983, -0.624187097320743, -0.9542804583459639, -1.2475336658998104, -1.4874201559497924, -1.6586037148598756, -1.748179038989984, -1.7469388284159018, -1.6505640442777934, -1.460619869323868, -1.1852345206882378, -0.839343929106235, -0.4444043057061633, -0.02750759297951205, 0.38011884624710546, 0.7451894731581545, 1.0349113866488315, 1.219839512212237, 1.2768069970191853, 1.1916554806880604, 0.9614655146588242, 0.5959917196864474, 0.11804515831585707, -0.4373614260565201, -1.0251836748452852, -1.5937767740100752, -2.089386233454288, -2.461349921422345, -2.6675344140306554, -2.679437228160302, -2.4863493555698617, -2.098002877500217, -1.5452328957430177, -0.8783595205698801, -0.1632323233973714, 0.5248452615977741, 1.1088108749526009, 1.5184013559831702, 1.6986277427958287, 1.6171299681275582, 1.269407635556709, 0.6810925995952549, -0.09327197182947657, -0.975078127032075, -1.869793327570981, -2.6775955440374766, -3.3053004602301477, -3.6781014473010356, -3.749547644351982, -3.5083046213406774, -2.9805806950843183, -2.22763240102225, -1.3384248899247004, -0.4182301692977745, 0.42540526220691394, 1.0974070689611897, 1.5284873600426159, 1.684963453321905, 1.5734304051090817, 1.2393411577525746, 0.7594566445978546, 0.2291100590717195, -0.2538706738890697, -0.6060769480739892, -0.7734731692609309, -0.7417515396203418, -0.5400680352970982, -0.2371502435446385, 0.069972905114296, 0.2730611505772265, 0.27288353133904497, -0.0008576682252510628, -0.5735088962615229, -1.4165107543459445, -2.4476099852790387, -3.540828021914967, -4.545044846980405, -5.308408885255552, -5.7045298921008625, -5.6558153476949915, -5.149532638728408, -4.243238559628281, -3.0579760815367445, -1.7598132795117434, -0.5325064048585162, 0.4541114098531501, 1.0743583732296524, 1.2698541212108927, 1.0609510491766694, 0.543816816259525, -0.12682995466233024, -0.7665560115176939, -1.1964747640244513, -1.2783095396395154, -0.9424028523188681, -0.2029414443775466, 0.8430035543414893, 2.0329000633453296, 3.1696060402532957, 4.059778677806538, 4.552232421328436, 4.56840545671534, 4.1184916020641325, 3.2995989740283216, 2.275974291137489, 1.2451323774531253, 0.39683966374006574, -0.12638633653646936, -0.25871530230494777, -0.023828241094846745, 0.471916930520714, 1.064723925834451, 1.5715902893597664, 1.833055574656629, 1.7507515346080524, 1.3109919034732371, 0.5886472540336307, -0.27000053790536443, -1.0818203732013019, -1.6709725807847238, -1.9122612569643038, -1.763182103797682, -1.2765187511635885, -0.5897696214690479, 0.10680122267800594, 0.6163901045234286, 0.7852596280598081, 0.5435368535445304, -0.07333157201151926, -0.928673463864927, -1.814374183215378, -2.500102938781742, -2.7906008868621104, -2.5771027202721024, -1.8697664504977505, -0.8021013594402205, 0.39505770489705827, 1.4450062702628443, 2.0904722712982857, 2.1572235529668435, 1.600200497417986, 0.5200943505052683, -0.8548315090209097, -2.218433304982672, -3.256705091235068, -3.7215311696102638, -3.490176554540004, -2.5956130601486884, -1.2197269192631304, 0.3494039915492418, 1.7859251549614743, 2.803453481413524, 3.22188385850982, 3.0069973526617124, 2.273014892535716, 1.247798924838262, 0.21014493748653618, -0.5840638443377922, -0.9671472477808073, -0.8990287954288341, -0.4704862008700912, 0.13007143206067834, 0.6765152875333778, 0.9743366440571177, 0.9194454211001265, 0.5293696995027435, -0.06238061055642787, -0.647415154536746, -1.0072409875580621, -0.9827091095740781, -0.527280518563858, 0.2725074514356531, 1.2167381756464362, 2.0476037274241436, 2.5254548674030723, 2.503433204388676, 1.9782035314312143, 1.10044003980426, 0.1399443837682771, -0.5865237464234112, -0.8052595911329704, -0.3679294294993904, 0.6981718995730151, 2.187892740087981, 3.7665913679939296, 5.0570118920448115, 5.740963963774555, 5.647051278986345, 4.798928936434469, 3.409402299032738, 1.821138160053786, 0.41039381260625274, -0.5186628439474501, -0.8182195383778588, -0.5346976843849734, 0.11130757148539218, 0.7974209901975505, 1.2028059515938823, 1.1113511543903396, 0.48323708882773303, -0.5274869298141684, -1.6155890139140974, -2.4155762321412406, -2.6138723122795184, -2.048323665959581, -0.7644448685985751, 0.9894050208282622, 2.8272911607133975, 4.3323241934887164, 5.172767041813255, 5.192726767744586, 4.450296584418243, 3.1922529891976423, 1.7740920615923825, 0.5511130238215547, -0.2249696716040926, -0.47163458722419666, -0.2837088885197945, 0.11668885530647269, 0.4700581001726842, 0.5778665598064663, 0.3753190686728419, -0.04666466089169331, -0.4780392874499988, -0.6722502969102374, -0.445970548708577, 0.23971021350230584, 1.2469095826356087, 2.291598084073727, 3.029926436474751, 3.1730620017935403], 'positive_zeros': ['4.43486437003440839041916273829583', '6.86705334043097671359123212326101', '8.476519061928771228668739641514085', '10.58724244716950306665003513673631', '11.93352692971075732567821740167594', '13.97056013694459173859190634953438', '15.37221282991038364890764394428090', '16.48025858588084541219955233813540', '17.05042483898276986362979849656570', '19.42381086195133821834902176725385'], 'prelabel': '2-15-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9407596133370679, 'root_angle': 0.2581164495936479, 'root_number': '0.688848657215489 + 0.724905185146594*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.129058224797', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.43486437003440839041916273830', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.86705334043097671359123212326', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '8.476519061928771228668739641514', 'prec': 107}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.8850286500861096, 'bad_primes': [3, 5], 'central_character': '5.4', 'conductor': 15, 'conductor_radical': 15, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/15/4/b/a/4/2'], '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': '2-15-5.4-c3-0-2', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-15-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9407596133370679, 'root_angle': 0.12905822479682394, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '4.43486437003440839041916273830', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '5621858480604906257651892621037', 'Lhash_array': ['5621858480604906257651892621037'], 'label': '2-15-5.4-c3-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/15/4/b/a/4/2'}