Formats: - HTML - YAML - JSON - 2026-05-31T06:43:24.225641
Query: /api/lfunc_lfunctions/?_offset=0
Show schema

{'Lhash': '3714632783824781256941511474666', 'a10': [1.7320508075688772, 0.0], 'a2': [1.7320508075688772, 0.0], 'a3': [-0.7320508075688773, 0.0], 'a4': [1.0, 0.0], 'a5': [1.0, 0.0], 'a6': [-1.2679491924311228, 0.0], 'a7': [0.7320508075688773, 0.0], 'a8': [-1.7320508075688772, 0.0], 'a9': [-2.4641016151377544, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6787284171808836, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-1.0, 0]]], [17, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [5, 17], 'central_character': '85.1', 'coefficient_field': 'CDF', 'conductor': 85, 'conductor_radical': 85, 'conjugate': '3714632783824781256941511474666', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.7320508075688772, 0], [2.0, 0]], [[1.0, 0], [0.7320508075688773, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.7320508075688773, 0], [7.0, 0]], [[1.0, 0], [-1.2679491924311228, 0], [11.0, 0]], [[1.0, 0], [4.0, 0], [13.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-5.464101615137754, 0], [19.0, 0]], [[1.0, 0], [-2.196152422706632, 0], [23.0, 0]], [[1.0, 0], [-3.4641016151377544, 0], [29.0, 0]], [[1.0, 0], [-6.732050807568878, 0], [31.0, 0]], [[1.0, 0], [7.464101615137754, 0], [37.0, 0]], [[1.0, 0], [-3.4641016151377544, 0], [41.0, 0]], [[1.0, 0], [7.464101615137754, 0], [43.0, 0]], [[1.0, 0], [0.9282032302755092, 0], [47.0, 0]], [[1.0, 0], [-6.0, 0], [53.0, 0]], [[1.0, 0], [-9.464101615137755, 0], [59.0, 0]], [[1.0, 0], [-8.928203230275509, 0], [61.0, 0]], [[1.0, 0], [10.0, 0], [67.0, 0]], [[1.0, 0], [5.660254037844386, 0], [71.0, 0]], [[1.0, 0], [14.392304845413264, 0], [73.0, 0]], [[1.0, 0], [16.588457268119896, 0], [79.0, 0]], [[1.0, 0], [-15.464101615137755, 0], [83.0, 0]], [[1.0, 0], [16.392304845413264, 0], [89.0, 0]], [[1.0, 0], [-8.928203230275509, 0], [97.0, 0]], [[1.0, 0], [2.5358983848622456, 0], [101.0, 0]], [[1.0, 0], [4.928203230275509, 0], [103.0, 0]], [[1.0, 0], [-0.33974596215561353, 0], [107.0, 0]], [[1.0, 0], [10.0, 0], [109.0, 0]], [[1.0, 0], [-17.320508075688775, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 9595062, 'index': 1, 'label': '2-85-1.1-c1-0-1', '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/85/2/a/c/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.429765515919452, 1.4402656023783345, 1.471080706900533, 1.5202487725403409, 1.5847663574072646, 1.6608672813326024, 1.7442589105973683, 1.830282819497271, 1.9140127298093959, 1.9903230765105209, 2.053961161089155, 2.099646295071873, 2.1222085419373093, 2.116770667148283, 2.0789699913578343, 2.0052114280258695, 1.8929385145247595, 1.7409054388604677, 1.5494299214771943, 1.3206045269205875, 1.0584428568653776, 0.7689374545140891, 0.46000844559733367, 0.14132618743511224, -0.1760024014837591, -0.47988567333421595, -0.7578287938865993, -0.997624953355711, -1.1881240443657333, -1.320034828941217, -1.3867063276431788, -1.3848265623449516, -1.3149730614275759, -1.1819507595495098, -0.9948599062801466, -0.7668497656780687, -0.5145331644603431, -0.25706165552206256, -0.014889886979358221, 0.19171125142436868, 0.3443025098613305, 0.4279676585448792, 0.4329099120734404, 0.35580346034257854, 0.20075074485810268, -0.020289380581074733, -0.2877082541077844, -0.5751510534385236, -0.8511242970083571, -1.0812500481234777, -1.2310422448739287, -1.2690158331543577, -1.169884116591252, -0.9175607921323078, -0.5076666668064251, 0.05074823899147709, 0.7345160523842766, 1.5068747449978301, 2.3192868483347264, 3.1145200000534308, 3.830830057209458, 4.406963012986103, 4.7875821421016065, 4.9286448459179955, 4.8022113472596795, 4.4001735924572785, 3.7364521142431166, 2.8473205749049253, 1.7896757797519445, 0.6372628568902864, -0.5249263098503955, -1.6076594553844266, -2.5252765479850607, -3.203582581697343, -3.5870346199881475, -3.644457498559586, -3.3726276782795357, -2.7972497567251744, -1.9711005691218921, -0.9694081894493746, 0.11716290749661719, 1.1912680360554304, 2.158503230434744, 2.936877540342401, 3.465095957160369, 3.7087046833329502, 3.6633591902878573, 3.354782393342946, 2.835353680032893, 2.1776673172332335, 1.4657728710123368, 0.785112490427522, 0.2123581411883934, -0.19360387424989775, -0.39840658382359806, -0.39578275738837665, -0.2075068484778386, 0.12032257789195154, 0.5241972204231614, 0.9324085597416674, 1.2753186509075174, 1.49528355182658, 1.5548350420518626, 1.4419364881188281, 1.1715143170847466, 0.7829808892270532, 0.334039807713531, -0.10837957903652762, -0.47875768483530895, -0.7236089245427395, -0.8104568222432019, -0.7337093638588839, -0.516399605510606, -0.20734986773779568, 0.12599176843470852, 0.40810668656541776, 0.5678383009088659, 0.5508134482241586, 0.32986393215097864, -0.08833509002047212, -0.6616963253179344, -1.3167796348840826, -1.9581791017730832, -2.482075197152057, -2.7920590623195567, -2.814861086933356, -2.5134873035150234, -1.8955261397712628, -1.01501727398557, 0.032803794861046995, 1.1234863131100352, 2.1205846845560106, 2.8957198003462783, 3.348497136444526, 3.423153177729647, 3.1191466457839963, 2.493717471136904, 1.6556008064817545, 0.7504383475985652, -0.060232547561828574, -0.6234258872099114, -0.8189209307174543, -0.5794436649102722, 0.09651253996092364, 1.1415318275515465, 2.426655114742307, 3.7785289451780755, 5.003984663923339, 5.918451490014374, 6.373884247276558, 6.281835684330938, 5.627956342631467, 4.4754781075783105, 2.956940982062422, 1.255287980178673, -0.4228238481428544, -1.8773571615624807, -2.9441001367490682, -3.5181159200116365, -3.567720720488767, -3.1368177202431347, -2.335333292055131, -1.3194762692670046, -0.26523186294712986, 0.6603861310267738, 1.3254671025903708, 1.6523706834071616, 1.6268489742207046, 1.2958512617778808, 0.7547639633891222, 0.12671715732654124, -0.4620219396272149, -0.9059059988890966, -1.1387792915530384, -1.1439853300204212, -0.9542237421426121, -0.6414782799168431, -0.2992794442135892, -0.021063157680182566, 0.12085562532587882, 0.09131614474738345, -0.10000338284410086, -0.40089015025741576, -0.7284575132806405, -0.9881094641827137, -1.09560279972001, -0.9974443249428877, -0.6850791777436509, -0.19950619071859435, 0.3751141370393642, 0.9279867311401955, 1.3452525196007734, 1.535844586854589, 1.4541297215506503, 1.1142138573389637, 0.5922641849516098, 0.015518182317364524, -0.46062765064238237, -0.6834715964146233, -0.5359187590134115, 0.035232943026947884, 1.0017881180967185, 2.2517665989503812, 3.6036642981330442, 4.8356222311425565, 5.724667751385924, 6.088906328108149, 5.824567521440388, 4.9304033110181, 3.5140528960349804, 1.7782684002446043, -0.011266413430954485, -1.5711411995831701, -2.6503353919300014, -3.0759032322816493, -2.7854499121815053, -1.8399267033645734, -0.4139119750134219, 1.2351697793201684, 2.8133442930670842, 4.043269441035625, 4.714237496240346, 4.719462674818931, 4.073540903072502, 2.906823382911769, 1.4379742328198069, -0.06972264040503032, -1.3595538081899483, -2.229884094831019, -2.5704386345292276, -2.379390912545914, -1.7582744986400543, -0.886308014878321, 0.02007198000930478, 0.7537166484457459, 1.1594620561730582, 1.164167040707448, 0.7881050189130123, 0.13583171864494487, -0.6308884766637161, -1.3316719090437876, -1.8088051595086971, -1.961998852736834, -1.7690013461384584, -1.287777493621726, -0.6401967706332155, 0.01861490790424999, 0.5378784064959277, 0.8068281201765389, 0.7801016949394389, 0.48699739249690926, 0.02258957128096147, -0.47699395406144574, -0.8690573689640558, -1.0401720976655944, -0.9346096890736504, -0.5683797816065653], 'positive_zeros': ['2.93032858041166400177262840993630', '4.75821808947205352603115115491298', '5.61469624409752576256081935993944', '6.86478368489459895603477435819298', '8.693059772496743559793207819410565', '9.986651261973227704823650504950746', '11.55816176180277487067958444215164', '12.08362200800634378347322471186154', '13.34314493158750539470958386483004', '14.20204190271550574769746759429759'], 'prelabel': '2-85-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8238497540091176, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.93032858041166400177262840994', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.75821808947205352603115115491', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.61469624409752576256081935994', 'prec': 103}}