Formats: - HTML - YAML - JSON - 2026-05-25T13:18:03.064950
Query: /api/lfunc_lfunctions/?_offset=0
Show schema

{'Lhash': '1174291874601583571071360045801', 'a10': [0.0, 0.0], 'a2': [1.0, 0.0], 'a3': [-1.79128784747792, 0.0], 'a4': [1.0, 0.0], 'a5': [0.0, 0.0], 'a6': [-1.79128784747792, 0.0], 'a7': [-2.79128784747792, 0.0], 'a8': [1.0, 0.0], 'a9': [0.20871215252208, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.182796232447249, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 23], 'central_character': '1150.1', 'coefficient_field': 'CDF', 'conductor': 1150, 'conductor_radical': 230, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.79128784747792, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.79128784747792, 0], [7.0, 0]], [[1.0, 0], [-3.79128784747792, 0], [11.0, 0]], [[1.0, 0], [1.20871215252208, 0], [13.0, 0]], [[1.0, 0], [-3.79128784747792, 0], [17.0, 0]], [[1.0, 0], [-1.20871215252208, 0], [19.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.58257569495584, 0], [29.0, 0]], [[1.0, 0], [-10.37386354243376, 0], [31.0, 0]], [[1.0, 0], [-4.0, 0], [37.0, 0]], [[1.0, 0], [2.20871215252208, 0], [41.0, 0]], [[1.0, 0], [-7.16515138991168, 0], [43.0, 0]], [[1.0, 0], [-13.58257569495584, 0], [47.0, 0]], [[1.0, 0], [6.0, 0], [53.0, 0]], [[1.0, 0], [4.41742430504416, 0], [59.0, 0]], [[1.0, 0], [3.37386354243376, 0], [61.0, 0]], [[1.0, 0], [-7.16515138991168, 0], [67.0, 0]], [[1.0, 0], [5.37386354243376, 0], [71.0, 0]], [[1.0, 0], [-14.74772708486752, 0], [73.0, 0]], [[1.0, 0], [-8.0, 0], [79.0, 0]], [[1.0, 0], [-6.0, 0], [83.0, 0]], [[1.0, 0], [3.16515138991168, 0], [89.0, 0]], [[1.0, 0], [14.9564392373896, 0], [97.0, 0]], [[1.0, 0], [-13.58257569495584, 0], [101.0, 0]], [[1.0, 0], [7.37386354243376, 0], [103.0, 0]], [[1.0, 0], [13.58257569495584, 0], [107.0, 0]], [[1.0, 0], [-10.37386354243376, 0], [109.0, 0]], [[1.0, 0], [6.0, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 20254924, 'index': 5, 'label': '2-1150-1.1-c1-0-5', 'leading_term': '1.61276903185111506937339482182', '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/1150/2/a/o/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.612769031851115, 1.6079596194818275, 1.5933986041007204, 1.5686961276999625, 1.5332300464602129, 1.4861852395977162, 1.4266047555716594, 1.3534496339858308, 1.2656641500407468, 1.1622434485502087, 1.0423009420844302, 0.9051333170783672, 0.7502814255934265, 0.5775856827849329, 0.3872348239346312, 0.17980701166469953, -0.04369764875786634, -0.2818340972502904, -0.5326996953489519, -0.7939328303633799, -1.0627235006453366, -1.3358364984266722, -1.6096476127379586, -1.8801930233136912, -2.1432317506432756, -2.3943206743939336, -2.628901242096651, -2.8423965743849924, -3.030317246281941, -3.1883736016556607, -3.3125920567485845, -3.399432486024948, -3.44590347702171, -3.449672007533657, -3.409163954358209, -3.323651802283153, -3.1933259969269545, -3.0193465842654024, -2.803872108323935, -2.550063197443739, -2.2620588548874534, -1.9449241724471007, -1.6045689920700357, -1.247637931082938, -0.8813731371980403, -0.5134521214888398, -0.15180399849288567, 0.19559159278731447, 0.5209177420723257, 0.8167397902236068, 1.0762246036903134, 1.2933526536173412, 1.4631157344181993, 1.5816931758314552, 1.6465996764182855, 1.6567984244605718, 1.6127739741919134, 1.5165604009133797, 1.3717215468054038, 1.183281658412109, 0.9576063647764542, 0.7022357005022482, 0.4256726809266495, 0.1371327210579423, -0.15373911423795433, -0.4371745059392183, -0.7036020952336899, -0.9439706822949196, -1.1500639244979525, -1.3147948033281542, -1.432468323872401, -1.499001565675186, -1.5120913211280729, -1.4713211206887173, -1.378201416700755, -1.2361390235171883, -1.050334516640805, -0.82760908671964, -0.5761652206854504, -0.30528842706884035, -0.024999914590643962, 0.2543274495343874, 0.5223755503927142, 0.7692939301072508, 0.9861023812985005, 1.1650661608626067, 1.3000272075212098, 1.3866759332093175, 1.4227500681807435, 1.4081496284568138, 1.3449602648340448, 1.2373809365927888, 1.0915558933240244, 0.9153151838955853, 0.7178321633117929, 0.5092105457810491, 0.30001726235194615, 0.1007805363492543, -0.07852498342109132, -0.2289826424690359, -0.34320380977228654, -0.41574009105064996, -0.44341592480131803, -0.4255624720928548, -0.36413744327502995, -0.263720136512838, -0.1313763253389517, 0.023606487495517102, 0.19010678354114674, 0.3556669003580632, 0.5070824054448931, 0.6310590572599104, 0.7149090460230075, 0.7472549348499141, 0.7187077828057261, 0.6224854863718648, 0.45493852221571895, 0.21595303839163024, -0.09079442687214576, -0.4577505479997447, -0.8735800786659388, -1.3234469562666542, -1.7894780241195867, -2.2513969129056743, -2.6873069534709346, -3.0745939180390147, -3.390912323529759, -3.615213367502901, -3.7287686431800156, -3.7161418652408194, -3.5660611173624703, -3.2721466917034694, -2.833454407846628, -2.2548012403687476, -1.5468489059885862, -0.7259314155130197, 0.18637595592551098, 1.1639367960746931, 2.1769612448512987, 3.193108225812158, 4.1787388650583335, 5.100269107539444, 5.9255630924352065, 6.625304985721789, 7.174285973342036, 7.552545144131593, 7.746308043691664, 7.74867461290686, 7.560018741760003, 7.188074333671083, 6.6476970272476805, 5.960305901042533, 5.153024863501346, 4.257558241613888, 3.308848569047333, 2.3435760227839117, 1.3985677340747398, 0.5091907906967426, -0.2921952120620801, -0.9776519166911453, -1.5248735388652028, -1.9181360909905953, -2.1489369698395637, -2.216292178366146, -2.1266751530997916, -1.8935989498446322, -1.5368614974653947, -1.0814908272048949, -0.5564427068361717, 0.006883892727779446, 0.5762383272707597, 1.120135717955894, 1.609417499403311, 2.0186749282501673, 2.3274623399328065, 2.52123785248763, 2.5919835661445325, 2.538474361636933, 2.3661832608245663, 2.0868309663722604, 1.7176065667172526, 1.2801043994144141, 0.7990376892838792, 0.3008019139553498, -0.18803083405937412, -0.6422014385850604, -1.0391532737335758, -1.3602434244375323, -1.5917077245298663, -1.7253260156722123, -1.7587515017415531, -1.6954877397374009, -1.5445175423207382, -1.319608661039718, -1.038340355093604, -0.720911671802211, -0.3888054471987544, -0.0633908492932151, 0.23544884744969397, 0.49057794121553266, 0.6886807121732035, 0.8210773112932978, 0.8842315909073155, 0.8799183826734305, 0.8150389731431446, 0.7010956890384539, 0.5533582213518663, 0.38977423107728043, 0.22969361942486982, 0.09248851012538732, -0.003841379998609047, -0.0439862750101632, -0.016478858211918298, 0.08539668180712008, 0.26300289654764764, 0.5120994612497577, 0.8229683674038116, 1.1809125712933677, 1.5671023771139645, 1.9597206742065756, 2.335337708481271, 2.670429715873025, 2.9429446155082206, 3.133812876212834, 3.2283030853556176, 3.2171297086870534, 3.0972346579705214, 2.8721837976790185, 2.552143275421807, 2.153427105934595, 1.6976351151661486, 1.2104273884089738, 0.7200059954298527, 0.2553953336614652, -0.15537248795587327, -0.48705230764640045, -0.7188444845334842, -0.8358075700675539, -0.8299288420971638, -0.7007765920077008, -0.45568355083664913, -0.10944015516902059, 0.3164923470668556, 0.7952076723618817, 1.295948670462667, 1.7859742122238713, 2.2325836942872135, 2.605171778435414, 2.8771818003589544, 3.027830630227635, 3.043490524782386, 2.9186339973107285, 2.6562747411847547, 2.267869510496806, 1.77268056715908, 1.1966335978700322, 0.5707395531647621], 'positive_zeros': ['0.926352951191884097594504054965189', '2.72054382036392625050348153692254', '3.71896873462567333673682235844971', '4.69270388701496293375701357770090', '5.71552343620791958133274735819723', '6.26098428855000817717282304546078', '6.89794079317323013227175124373740', '7.957169036281539429774128180975950', '9.235552577769392690316669871255227', '9.901638178568965617970020386985597'], 'prelabel': '2-1150-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.03031289348926, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.926352951191884097594504054965', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.72054382036392625050348153692', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.71896873462567333673682235845', 'prec': 103}}