-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '486654467602189923758740144998', 'a10': [0.9257481982667206, 2.0354336818982635], 'a2': [-0.7071067811865476, -0.7071067811865476], 'a3': [-2.8651360193508317, -1.186778197258777], 'a4': [0.0, 1.0], 'a5': [-2.093871787791391, -0.7846661304601374], 'a6': [1.186778197258777, 2.8651360193508317], 'a7': [1.093596876895019, 2.6401764119688154], 'a8': [0.7071067811865476, -0.7071067811865476], 'a9': [4.679241576333094, 4.679241576333094], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3574568343617672, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]], [5, [[1.0, 0], [2.093871787791391, 0.7846661304601374]]], [17, [[1.0, 0], [1.1069987757957154, -3.971719238615286]]]], 'bad_primes': [2, 5, 17], 'central_character': '170.59', 'coefficient_field': 'CDF', 'conductor': 170, 'conductor_radical': 170, 'conjugate': '2028215038042492131603750079683', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [2.8651360193508317, 1.186778197258777], [2.1213203435596424, 2.1213203435596424]], [[1.0, 0], [2.093871787791391, 0.7846661304601374]], [[1.0, 0], [-1.093596876895019, -2.6401764119688154], [-4.949747468305833, 4.949747468305833]], [[1.0, 0], [0.5436607702515783, 1.3125132048715638], [-7.7781745930520225, 7.7781745930520225]], [[1.0, 0], [-3.10929670091345, 0], [13.0, 0]], [[1.0, 0], [1.1069987757957154, -3.971719238615286]], [[1.0, 0], [5.836855257966118, -5.836855257966118], [0, -19.0]], [[1.0, 0], [4.30542572511801, -1.7833657271338965], [16.263455967290593, -16.263455967290593]], [[1.0, 0], [-4.05552030360273, -1.6798515122317028], [20.506096654409877, 20.506096654409877]], [[1.0, 0], [0.05835648181016301, -0.14088500983847435], [-21.920310216782973, -21.920310216782973]], [[1.0, 0], [3.1132168629531303, 1.2895366472438077], [26.16295090390226, 26.16295090390226]], [[1.0, 0], [3.2811166206965234, -1.3590830040202782], [28.991378028648448, -28.991378028648448]], [[1.0, 0], [-0.136165551360262, 0.136165551360262], [0, -43.0]], [[1.0, 0], [5.421729100963405, 0], [47.0, 0]], [[1.0, 0], [-6.743767121271339, -6.743767121271339], [0, 53.0]], [[1.0, 0], [-1.9748437531985403, -1.9748437531985403], [0, 59.0]], [[1.0, 0], [8.952652014052248, -3.7083098834272463], [43.1335136523794, -43.1335136523794]], [[1.0, 0], [0, -6.86630320696934], [-67.0, 0]], [[1.0, 0], [-1.403466694496704, 3.38826832819288], [-50.204581464244875, -50.204581464244875]], [[1.0, 0], [-4.327206589938834, 10.446800836620566], [-51.61879502661797, -51.61879502661797]], [[1.0, 0], [-4.2326269687056755, -10.218465432315362], [-55.86143571373726, 55.86143571373726]], [[1.0, 0], [3.182643798450012, 3.182643798450012], [0, 83.0]], [[1.0, 0], [0, 0.6198004900291987], [-89.0, 0]], [[1.0, 0], [5.758191572198207, -13.901504188343367], [-68.58935777509511, -68.58935777509511]], [[1.0, 0], [15.746386309057543, 0], [101.0, 0]], [[1.0, 0], [0, 7.010193915238237], [-103.0, 0]], [[1.0, 0], [1.9496445143271417, -4.706858228294891], [-75.66042558696059, -75.66042558696059]], [[1.0, 0], [11.00175915040133, -4.557077850058531], [77.07463914933368, -77.07463914933368]], [[1.0, 0], [6.738595790024271, -2.791217767578294], [79.90306627407988, -79.90306627407988]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-170-85.59-c1-0-0', '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/170/2/n/b/59/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.274175863479071, 0.19910217766451663, 0.11205898312003416, 0.0081821187393046, -0.11797423825967993, -0.2719609844106971, -0.45899934553225163, -0.6835865722883339, -0.9491208221241586, -1.257527768927856, -1.6088868736726951, -2.001071964249312, -2.4294340336608524, -2.886562791187177, -3.362167572682507, -3.843117904232831, -4.313679298174352, -4.755970642849439, -5.15065585623181, -5.477864653308149, -5.718316121925073, -5.854595624514404, -5.872512175052642, -5.762442157534549, -5.5205486242519, -5.149756081387687, -4.660361066866099, -4.070170848049617, -3.4040872458245097, -2.6930897898924093, -1.9726205944275306, -1.2804294744172773, -0.6539974040634984, -0.12771372920337276, 0.26996892807429645, 0.5191450877172193, 0.6105637226400623, 0.5469789070074955, 0.3435339439645832, 0.027041228695419757, -0.36588313726754645, -0.7917568102012307, -1.204046462667488, -1.5575513436004282, -1.812950448615887, -1.941047215625668, -1.9262297922439426, -1.7687024352548861, -1.485136920527706, -1.1075378371348945, -0.6803012069593527, -0.2556543517761393, 0.1121265338435582, 0.3731418616577956, 0.4882266964093913, 0.434473560930152, 0.2091843371501396, -0.16835700748666924, -0.6576825283668019, -1.2006135789796426, -1.7271855494540638, -2.1634704495857098, -2.4404553011505286, -2.502929864776557, -2.317252341741229, -1.8769192820606515, -1.205071620108587, -0.3534081650847857, 0.6025835246237979, 1.5716830348218018, 2.457414271918538, 3.1696924165022646, 3.636148379264017, 3.8115893015239766, 3.6842187226859693, 3.27761271744762, 2.6479907426980285, 1.8769658114066623, 1.0606204773251295, 0.29633570939378373, -0.33079404394850137, -0.7599687027511867, -0.9632556656773024, -0.9492954068193693, -0.7613788641045168, -0.469968639950633, -0.16061072500473425, 0.08103450848988128, 0.1847543545054646, 0.10942027963909767, -0.1476621104519596, -0.547502136728424, -1.0132058698323354, -1.4406343578468634, -1.7146428943589962, -1.72860051149033, -1.4041910094329682, -0.7082425579467148, 0.33640528571644535, 1.6482183222423352, 3.093504201253041, 4.501772760455087, 5.688066885900446, 6.479167617866221, 6.739768290433252, 6.394497886563407, 5.442123383195775, 3.959336322539175, 2.0930834784981682, 0.042198922808522284, -1.9691554230112018, -3.722328768084753, -5.034580569467873, -5.784271835046996, -5.92682803418731, -5.49889633880543, -4.61003318261383, -3.4233238442410565, -2.1281976642583498, -0.9100281150163805, 0.0783511525717627, 0.7384387001283285, 1.0375974600919775, 1.008612817381948, 0.7377366697188481, 0.3437733558054823, -0.04761178900955092, -0.3293403841833358, -0.4332211047146325, -0.34126252841788574, -0.08597992763625362, 0.2600926241744062, 0.6032701429374209, 0.8518167245999759, 0.9382282484864226, 0.835782693424105, 0.5656121353349814, 0.19254081353392571, -0.18964620505262658, -0.48048486643281757, -0.5978585713975909, -0.5001470183696678, -0.20024587877874783, 0.23226185295382154, 0.6820807511829774, 1.0107873847499538, 1.0868272028047132, 0.8168217778032225, 0.17138543678641596, -0.8006245458037311, -1.9734248366449676, -3.1621312147587, -4.1545850542145875, -4.751548150236945, -4.807510257470222, -4.2637392114049835, -3.1663089245955898, -1.6645242451008255, 0.011059344038591, 1.5876875726004507, 2.799554541940193, 3.437704403095489, 3.3908105346855613, 2.668434898127645, 1.401634980218144, -0.17978218126366943, -1.7893480336750227, -3.1373399450763344, -3.9850360947613894, -4.189016571892165, -3.7266214870819008, -2.6974751523875025, -1.3009002817599018, 0.20595124717382282, 1.560405476290302, 2.5460102547499206, 3.032913521549383, 2.998609176843821, 2.525123272015671, 1.7739145359747577, 0.9446766463812295, 0.2277520301552618, -0.23880793006119314, -0.3976935170787022, -0.279914799620254, 0.009923954799356656, 0.3267723442864882, 0.528386329248743, 0.5178605085706206, 0.2746620741263321, -0.13397673343712022, -0.5648025610683678, -0.8313192805912673, -0.7502683684624502, -0.1908752978641612, 0.8851466535447763, 2.4030612952784156, 4.1799809226808815, 5.955244831168169, 7.440371398370142, 8.377852661766294, 8.595673055143635, 8.0450822590585, 6.8127490168989215, 5.1041728905407195, 3.2018058687880204, 1.4071831716587127, -0.019922587404433936, -0.9116412694217817, -1.2203248088396936, -1.019144405952925, -0.47567433072315923, 0.19442020832512769, 0.7818368148834905, 1.1327579533385452, 1.1807981728301047, 0.9545099409647939, 0.5595555371151901, 0.14120754792855902, -0.16210396314794318, -0.26123991279119, -0.1430217419101591, 0.12632015222215623, 0.42198198607746734, 0.600005738848409, 0.5442369363478422, 0.20732354945260223, -0.36655611768713064, -1.0449259181605646, -1.6369594723949432, -1.9434358113036432, -1.8140020962641232, -1.1962015010570175, -0.1619523353034158, 1.097665364497126, 2.3105270065985377, 3.186966758632416, 3.493892472514547, 3.120939874227611, 2.120927834440084, 0.7123597582566786, -0.7593432270028797, -1.8949334353913874, -2.332803122947901, -1.8374773728554366, -0.36350788037813786, 1.9217475934083876, 4.66357934620192, 7.389276395152551, 9.606331784533989, 10.907200615383056, 11.056376104544695, 10.039515330506525, 8.06330109900621, 5.5064844865239, 2.834196579347066, 0.49623831571132976], 'positive_zeros': ['0.38390268384251310573464431517999', '4.16068987298866126547057739492319', '4.88427802460869437558570727817926', '6.45865240777440390613143245868585', '7.07461338252325226812443431096851', '8.422200898126333143645935173648216', '9.929849322580384488969104974249616', '10.82633346173900777907170876387540', '11.18852561939638490130938015138086', '12.21360816866927195653590450311007'], 'prelabel': '2-170-85.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1650994954774323, 'root_angle': -0.32352616132824685, 'root_number': '0.526440844882406 - 0.850211759998354*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.161763080664', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.38390268384251310573464431518', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.16068987298866126547057739492', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.88427802460869437558570727818', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.3574568343617672, 'bad_primes': [2, 5, 17], 'central_character': '85.59', 'conductor': 170, 'conductor_radical': 170, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/170/2/n/b/59/1'], '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': '2-170-85.59-c1-0-0', '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': '2-170-85.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1650994954774323, 'root_angle': -0.16176308066412343, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.38390268384251310573464431518', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '486654467602189923758740144998', 'Lhash_array': ['486654467602189923758740144998'], 'label': '2-170-85.59-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/170/2/n/b/59/1'}