-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2804557660621333054697166581802', 'a10': [-0.5828784078430391, 1.0095750170189974], 'a2': [0.1917306213155015, -1.8241950082302185], 'a3': [-1.4712116049697712, -1.6339460204413705], 'a4': [-1.3346315954344077, -0.28368470302171367], 'a5': [-0.5806055886118833, -0.2585022629004576], 'a6': [-3.262712489314209, 2.3704993801410095], 'a7': [2.399845217995372, -1.1138864078822157], 'a8': [0.3602386673554215, -1.1087006159737332], 'a9': [-0.1917306213155015, 1.8241950082302185], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.763329051202452, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-2.399845217995372, 1.1138864078822157]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [7, 11], 'central_character': '847.81', 'coefficient_field': 'CDF', 'conductor': 847, 'conductor_radical': 77, 'conjugate': '643889779513488069734318506902', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.1917306213155015, 1.8241950082302185], [-1.9562952014676114, -0.4158233816355187]], [[1.0, 0], [1.4712116049697712, 1.6339460204413705], [-0.3135853898029604, 2.98356568610482]], [[1.0, 0], [0.5806055886118833, 0.2585022629004576], [3.345653031794291, 3.715724127386971]], [[1.0, 0], [-2.399845217995372, 1.1138864078822157]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.4572893961119622, 1.0587827218865906], [4.017220926874317, 12.363734711836996]], [[1.0, 0], [0.296259084583155, 2.818716903598492], [-16.628509212474697, 3.5344987439019087]], [[1.0, 0], [5.4415713615016195, -1.1566416986828452], [17.35736369520942, -7.727996218440204]], [[1.0, 0], [1.0828784078430391, 1.875600420803436], [-11.5, 19.91858428704209]], [[1.0, 0], [-3.223145183408803, -9.919820868902985], [-23.461492836873475, 17.04577231648172]], [[1.0, 0], [-5.874386808774484, 2.6154455158644705], [20.743048797124604, -23.037489589799222]], [[1.0, 0], [-4.0588585054809805, 4.507819052108091], [-3.8675531409031785, -36.797310128626115]], [[1.0, 0], [2.3286482339576176, -7.1668423335235865], [-33.16969676937284, -24.099195343991397]], [[1.0, 0], [-4.86717761214384, 0], [43.0, 0]], [[1.0, 0], [-2.7723081706328037, 0.5892722926394178], [42.936636509202245, -19.116622224562608]], [[1.0, 0], [-6.823997406066771, 3.0382393936519696], [35.46392213701949, -39.3866757503019]], [[1.0, 0], [11.548761656995806, 2.4547650693576157], [53.899182000913456, 23.997461941472213]], [[1.0, 0], [-3.957034602657041, -1.7617853138613802], [40.81696698789035, 45.33183435412105]], [[1.0, 0], [-0.8013087564840029, 1.38790747878013], [-33.5, -58.023702053557386]], [[1.0, 0], [3.472329596147113, -2.5227951228525574], [21.940206600621266, -67.52501265695591]], [[1.0, 0], [15.64396082666703, 3.325226524216861], [66.68881840790986, 29.691774944533414]], [[1.0, 0], [-0.4977468293388182, 4.7357447402632475], [-77.27366045797065, -16.42502357460299]], [[1.0, 0], [7.468542053826879, -5.426213424301731], [25.648410533120636, -78.93769085249775]], [[1.0, 0], [0.1822240296010377, 0.31562127762893233], [-44.5, 77.07626093681505]], [[1.0, 0], [-2.100267766663693, -1.525933852680013], [29.974648454369902, 92.2524820806299]], [[1.0, 0], [-9.044202384270852, 4.0267383372132395], [67.58219124224468, -75.05762737321682]], [[1.0, 0], [-4.16977146406912, 4.63100037197281], [-10.766431716568308, -102.43575522293216]], [[1.0, 0], [-10.85626780276199, 2.3075709567240543], [97.7493639677583, -43.520820809110624]], [[1.0, 0], [7.152019154712884, -12.38766055266853], [-54.5, -94.39676901250381]], [[1.0, 0], [2.6851778048456594, -8.264127524361871], [-91.41892036436906, -66.41973350904946]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 59, 'label': '2-847-77.4-c1-0-59', '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/847/2/n/d/81/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.9749665581692574, 1.2844622033559487, 1.630652770652615, 2.015914729473162, 2.4379204128062866, 2.888106827436997, 3.3508501093302168, 3.8033579781884397, 4.216275866293341, 4.555024459164005, 4.781887783489449, 4.858828447269396, 4.75092418663769, 4.430213562953606, 3.8796281950509472, 3.0965946842612544, 2.095831117010495, 0.9108581485078903, -0.4061940068596417, -1.7867683455764583, -3.150138886715047, -4.409576683267965, -5.479980347127072, -6.286262345694646, -6.771571113632446, -6.904313462001067, -6.682956422786126, -6.137752625781605, -5.3288479845383945, -4.340669812264195, -3.273007738791016, -2.229718612610195, -1.3064275852278255, -0.5788786996550999, -0.09364216150744958, 0.13732633305731923, 0.13725431212206554, -0.04007969462181476, -0.3196945958456272, -0.6181769166344875, -0.8579147605011279, -0.9804541529070343, -0.956631861970219, -0.7915539519823429, -0.5232911830029473, -0.21524100919921108, 0.05671408977770394, 0.22005584077867046, 0.2215551381051578, 0.040112026504480064, -0.3062768728779674, -0.7612508497277264, -1.2389325718791013, -1.639682891406964, -1.8700330658165418, -1.8629660623113165, -1.5943138956308573, -1.0914801670438923, -0.43197712235611957, 0.2688029376096593, 0.8789270455590268, 1.2766245825762554, 1.377119954266257, 1.1538592411189093, 0.6490828260993797, -0.029461286677563807, -0.7261617890304995, -1.266982771128247, -1.4953552985867768, -1.3073225586327026, -0.6782956919392251, 0.32502668233661824, 1.5513071989900378, 2.789756567515242, 3.8097693270022477, 4.407447180969448, 4.44939072593322, 3.9040737361683417, 2.8532098136151554, 1.4794696511779193, 0.031948668314549386, -1.2241520329014657, -2.063242688326662, -2.348265712548759, -2.06150301608445, -1.3094874752845227, -0.29978031869391303, 0.7062377303014046, 1.4546309807664386, 1.7605175799320882, 1.5555459475905762, 0.9093713042008805, 0.018821899458416332, -0.834210042624062, -1.347642649380044, -1.2725145373871098, -0.4777211880422121, 1.0095709791166962, 2.998494622765806, 5.166839269595708, 7.125153555745139, 8.49881872849562, 9.00962975111015, 8.53802039281368, 7.151196969818542, 5.09022459356063, 2.718724772849544, 0.4449656792914973, -1.3645114877081468, -2.45961146303578, -2.7525918425228575, -2.325199221845348, -1.3967146161265083, -0.2622157338672631, 0.7824956312248694, 1.5100440186313864, 1.8076865684457077, 1.6902021145406432, 1.2783318173549234, 0.7509439757959064, 0.285909959773392, 0.007139450861866185, -0.04731182012763564, 0.07209518613631453, 0.2521200032483677, 0.36148183089926017, 0.29959695757738364, 0.033355580994807954, -0.3900129871139654, -0.8581561924995346, -1.2318796709306612, -1.3937535764299482, -1.290530624035526, -0.9543805587327339, -0.4944736382766123, -0.060100330848649866, 0.21367710381200947, 0.2600668372416632, 0.11516213769048556, -0.08109379657147911, -0.12179944749464204, 0.20023864743766837, 1.0149303079172507, 2.3109766149212128, 3.9085064651540358, 5.482076807300693, 6.633479205752902, 6.9982073172971795, 6.357341855554132, 4.7220112694950425, 2.362504798340083, -0.23218255772477958, -2.4595521334448, -3.7496414219512033, -3.7145106398253924, -2.2602420988786873, 0.37145476045277664, 3.647051063504601, 6.862395217984801, 9.311528157229287, 10.459238760578689, 10.071355925885905, 8.267604909313581, 5.482839901998459, 2.3477408932676225, -0.47762401058072196, -2.471131834630448, -3.37103480288202, -3.221308834362664, -2.3305160048418707, -1.1599207809658414, -0.176610860502183, 0.2836863077977125, 0.10407317665797, -0.5991393927192992, -1.5352378312800843, -2.3485984208490662, -2.7415124244064923, -2.5703822633241526, -1.885534664372665, -0.9043695649368054, 0.07019601140410485, 0.7563419383850425, 0.9879765834834217, 0.765526044852285, 0.24684416291228456, -0.3168132718092033, -0.6758628734385361, -0.6741918403546282, -0.3049683336371649, 0.28918740664042464, 0.8713808729616707, 1.2008340050321358, 1.1255929388307657, 0.6435488267938921, -0.09117432969034649, -0.8199632500411942, -1.2720576302917097, -1.264830419124543, -0.7756503535225192, 0.041721732319355824, 0.9039787320400237, 1.4935636054670651, 1.5697755406212859, 1.056442168258215, 0.07422340313452237, -1.095421229854622, -2.1034523469724244, -2.651778508838504, -2.5954302085641885, -1.9917062501420697, -1.0779731780350694, -0.18523240783972902, 0.38196180224934917, 0.4557555857748296, 0.06464588965988144, -0.5804554627673335, -1.1699082780818992, -1.418686179260287, -1.183320777882996, -0.527058605986176, 0.29442590226510335, 0.9254611903973761, 1.0497277170089578, 0.5255011334151986, -0.5360133299652889, -1.7841720520733872, -2.7370848499617884, -2.9521794753853547, -2.201181344613289, -0.585418867911559, 1.4558982105820217, 3.25689071588534, 4.126622560575742, 3.5782529111648547, 1.509238771594935, -1.7316071148755718, -5.419305172404884, -8.652612778903134, -10.618638536020391, -10.838613364754996, -9.315247548742901, -6.532898839347573, -3.309383683740606, -0.5467169338884745, 1.0390793087265104, 1.1228922546416642, -0.153323406302185, -2.253053476528242, -4.436963320966105, -6.006256951537838, -6.515856948297889, -5.889643673063523, -4.406531402000654, -2.5717141511996098, -0.9257010821886011, 0.1384016250815557], 'positive_zeros': ['2.21240589490226800779003607244134', '4.28663352352746340415933292172858', '4.60348599439188198001003139194163', '5.72058125587844047580369639787847', '6.14277375949301595936347171538299', '7.32643851677349390559071962292078', '8.119854986087729526891912560485022', '8.838400223601673511897570665223639', '10.00286836694432510214587553617735', '10.78573494515355923555615280034127'], 'prelabel': '2-847-77.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6006401233547196, 'root_angle': -0.6041546110431499, 'root_number': '-0.3214036011751086 - 0.9469423029687034*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.302077305522', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.21240589490226800779003607244', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.28663352352746340415933292173', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.60348599439188198001003139194', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 6.763329051202452, 'bad_primes': [7, 11], 'central_character': '77.4', 'conductor': 847, 'conductor_radical': 77, 'degree': 2, 'index': 59, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/847/2/n/d/81/3'], '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': '2-847-77.4-c1-0-59', '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': '2-847-77.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6006401233547196, 'root_angle': -0.30207730552157497, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.21240589490226800779003607244', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2804557660621333054697166581802', 'Lhash_array': ['2804557660621333054697166581802'], 'label': '2-847-77.4-c1-0-59', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/847/2/n/d/81/3'}