-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2519337409496285549533435044771', 'a10': [-1.2477538283024623, 2.161173025958438], 'a2': [2.161173025958438, 1.2477538283024623], 'a3': [1.4134191976559758, -2.4481138627333876], 'a4': [2.113779232086901, 3.661173025958438], 'a5': [0.0, 1.0], 'a6': [6.109286888691825, -3.5271984297428767], 'a7': [1.6499623486199286, -0.9526062061284629], 'a8': [0.0, 5.558889202880829], 'a9': [-2.4955076566049246, -4.322346051916876], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.747358970798196, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, -1.0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 13], 'central_character': '845.316', 'coefficient_field': 'CDF', 'conductor': 845, 'conductor_radical': 65, 'conjugate': '2294746747384715426960851019130', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.161173025958438, -1.2477538283024623], [1.0, 1.7320508075688772]], [[1.0, 0], [-1.4134191976559758, 2.4481138627333876], [-1.5, -2.598076211353316]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [-1.6499623486199286, 0.9526062061284629], [3.5, -6.06217782649107]], [[1.0, 0], [0.9261183264501012, 0.5346946650774116], [5.5, 9.526279441628825]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.3186316099129015, -0.5518861372666126], [-8.5, 14.722431864335457]], [[1.0, 0], [4.964101615137754, -2.866025403784439], [9.5, -16.454482671904334]], [[1.0, 0], [-1.9089268542609004, 3.306358299512509], [-11.5, -19.91858428704209]], [[1.0, 0], [4.727558464173802, -8.188371455701315], [-14.5, -25.11473670974872]], [[1.0, 0], [0, -1.4641016151377546], [-31.0, 0]], [[1.0, 0], [0.6559701324988475, 0.3787245325785641], [18.5, 32.04293994002423]], [[1.0, 0], [-0.2320508075688773, -0.13397459621556135], [20.5, 35.50704155516198]], [[1.0, 0], [-0.3186316099129015, -0.5518861372666126], [-21.5, 37.239092362730865]], [[1.0, 0], [0, 9.446132241557452], [-47.0, 0]], [[1.0, 0], [6.991015313209849, 0], [53.0, 0]], [[1.0, 0], [-0.6417555632208786, 0.37051774717951413], [29.5, -51.09549882328188]], [[1.0, 0], [2.09927993113815, 3.6360595000409694], [-30.5, 52.827549630850754]], [[1.0, 0], [-7.010291689224458, -4.047393793871537], [33.5, 58.023702053557386]], [[1.0, 0], [8.456632368831448, -4.882438974582539], [35.5, -61.48780366869514]], [[1.0, 0], [0, 3.7164888735582426], [-73.0, 0]], [[1.0, 0], [9.319369149005643, 0], [79.0, 0]], [[1.0, 0], [0, 5.1177784057616575], [-83.0, 0]], [[1.0, 0], [-10.893156482200729, -6.2891668273233075], [44.5, 77.07626093681505]], [[1.0, 0], [-3.6559701324988474, 2.1107753401474416], [48.5, -84.00446416709055]], [[1.0, 0], [7.623786189640577, -13.204785026499415], [-50.5, -87.4685657822283]], [[1.0, 0], [-13.526913698072095, 0], [103.0, 0]], [[1.0, 0], [-3.6813683900870986, 6.376317093008897], [-53.5, -92.66471820493493]], [[1.0, 0], [0, 10.075966577375306], [-109.0, 0]], [[1.0, 0], [-3.3440298675011526, -5.792029632539817], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 42, 'label': '2-845-13.4-c1-0-42', '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/845/2/m/g/316/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [4.70859480524201, 4.711447515338371, 4.718344960702102, 4.718077519230847, 4.694109159023421, 4.627558979428184, 4.500225650159923, 4.297256765106167, 4.009301159011145, 3.634089319970352, 3.177392243141012, 2.653281803823738, 2.083606637873793, 1.4966277690565846, 0.9248286110711328, 0.40201421388230246, -0.0400714788483843, -0.375273542588296, -0.5862809138489746, -0.6671547835908329, -0.6247038741842383, -0.4783767504225946, -0.25850636317285597, -0.002961476953030575, 0.2474924060559118, 0.4545795025231785, 0.587913144858031, 0.6295728062751023, 0.5770462390162723, 0.4438882270002779, 0.2577482439620407, 0.05582693413000686, -0.12171903015641992, -0.23946677431513316, -0.27422312251617037, -0.22089066950130642, -0.0953632493864954, 0.06652979711943798, 0.21440950687465976, 0.292672677788833, 0.252546697327057, 0.0649423029337109, -0.2682969820353827, -0.7072371415210609, -1.172902091332695, -1.5538053563840653, -1.7200288400011692, -1.5434972376439038, -0.921719616322278, 0.19879957649270058, 1.8037892428449496, 3.801164651429502, 6.022768064189139, 8.239228512918475, 10.187066093963093, 11.604845480385205, 12.273176656653174, 12.052088641547371, 10.909091627426655, 8.932251975259666, 6.324768544945857, 3.3805593170966297, 0.44374559422338666, -2.141961773133224, -4.0857398368239215, -5.194924055063487, -5.404829583773744, -4.787332781344544, -3.5361244372325014, -1.9308434862775508, -0.2863687299564964, 1.1034459076380763, 2.017025492927842, 2.341541025377517, 2.087605164946711, 1.3795089415829318, 0.42326666032068555, -0.5406779319752191, -1.2900095849158852, -1.6671713728516406, -1.610165902525193, -1.1611082554725454, -0.45105961550063933, 0.33499448496646406, 1.0046440701290023, 1.4050230643362143, 1.459139637338013, 1.1829796065211415, 0.6793847843673393, 0.11031683085631669, -0.3455912779792774, -0.5396188740944804, -0.3919822639562295, 0.08661501579312482, 0.796524019544216, 1.5736073674975386, 2.230577528000323, 2.6047594810569286, 2.6000070428352853, 2.2118353770406114, 1.5290473143675567, 0.7111977908397098, -0.05239460145349138, -0.5914021815102313, -0.7981019586606095, -0.6541539306463944, -0.23326093858969196, 0.3210764393854656, 0.8366436106511462, 1.1610496464285773, 1.2040856791190568, 0.9618257291253581, 0.5154385191525839, 0.004898421905551572, -0.4148250446013033, -0.6221015622445722, -0.5667335827283763, -0.2856280129999104, 0.10974113766157026, 0.4713587814834954, 0.6672711312229298, 0.6324706089778431, 0.4010276750396809, 0.10690812393893806, -0.0503342774124029, 0.13193859025303714, 0.7853350686222498, 1.9068688021258706, 3.3275469428943545, 4.727617262770556, 5.70081346736104, 5.855785514385225, 4.930686688226968, 2.890306894545245, -0.023423394130039663, -3.3069917260414075, -6.280349322183301, -8.226550909399073, -8.555353290995416, -6.9514618286829215, -3.469320432740005, 1.4523190669343828, 7.063856366547513, 12.452291297001404, 16.729597328537572, 19.21791410878704, 19.587547122034337, 17.915199378423168, 14.649765151219055, 10.496163176650889, 6.24791295459912, 2.61107064525381, 0.0626368182273726, -1.2243058406657834, -1.375452389001013, -0.7385366742944801, 0.23832449829156935, 1.1366143899558339, 1.6700288875637093, 1.7349327309642966, 1.401113926533227, 0.8534289492953663, 0.3084820032562851, -0.06441525519815708, -0.19318520212439316, -0.11101019859728256, 0.07509584639394704, 0.23935040323718632, 0.2930193000709779, 0.2194778753197351, 0.07601896954489916, -0.036842087086371114, -0.025170288709065354, 0.15032668390377318, 0.4483489205290443, 0.7552323551050766, 0.9262204365603365, 0.8453504964558859, 0.48111663262271404, -0.08507034453459789, -0.6719767376298494, -1.0528321071058142, -1.034710470410194, -0.5358857647861661, 0.36788360446117097, 1.4486264726472138, 2.386723708644622, 2.870955338833046, 2.7066408047857977, 1.8947152170837462, 0.651420993090169, -0.6437006591328499, -1.560102277557865, -1.7557454161151145, -1.0988429418546783, 0.2706063420266518, 1.9647521867904765, 3.4556503634605495, 4.2370557668878295, 3.9905195784451815, 2.7015117810113356, 0.6845414385017619, -1.496168394193794, -3.1904327605654785, -3.861762640868091, -3.260537911009697, -1.5142783885690714, 0.8967778937536101, 3.2747414720602466, 4.910108687795606, 5.295396258704785, 4.279325562819077, 2.1125188990730908, -0.6301346636139867, -3.2258898691200932, -5.023082749611088, -5.632873945217288, -5.033397322977525, -3.555017432996465, -1.754629475347442, -0.22318905639374323, 0.6081930662609579, 0.5992380797878908, -0.07317068855682332, -0.9986734641288084, -1.6948914663188768, -1.7884789216343868, -1.1521159106986731, 0.04958987467829858, 1.4196518138451721, 2.470927767589972, 2.7996805403760217, 2.229037323806203, 0.8725462780860135, -0.9030415609704693, -2.600923658987951, -3.758762311548996, -4.096691961966829, -3.598442673885663, -2.500342572262701, -1.1962780305954095, -0.09596699914362083, 0.5113300417689605, 0.5401834811555801, 0.11367602933104166, -0.5062400226439717, -1.0312801904175108, -1.2568930237007494, -1.1284556317551682, -0.7418722398572901, -0.2840022510739458, 0.05795507144117401, 0.17807167020749534, 0.0901534391181306, -0.091173223947539, -0.2155546251948253, -0.17679437167572384], 'positive_zeros': ['1.98740678941239872205744928434972', '2.87642520884560957235645193863773', '3.91131876622579047076076689003982', '4.57469762509582880872991030435355', '5.15391193544780901055499744567950', '6.10638173614328839718757741654821', '7.76990870134379619565013455678903', '8.773308352090656109912569931691116', '9.553206969779963737859503061411837', '10.32118273033138095247282438058114'], 'prelabel': '2-845-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5975678953201964, 'root_angle': -0.08129238194076664, 'root_number': '0.9675654653395972 - 0.2526204074934736*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0406461909704', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.98740678941239872205744928435', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.87642520884560957235645193864', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.91131876622579047076076689004', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 6.747358970798196, 'bad_primes': [5, 13], 'central_character': '13.4', 'conductor': 845, 'conductor_radical': 65, 'degree': 2, 'index': 42, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/845/2/m/g/316/4'], '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': '2-845-13.4-c1-0-42', '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': '2-845-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5975678953201964, 'root_angle': -0.04064619097038332, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.98740678941239872205744928435', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2519337409496285549533435044771', 'Lhash_array': ['2519337409496285549533435044771'], 'label': '2-845-13.4-c1-0-42', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/845/2/m/g/316/4'}