-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': -1, 'A3': 1, 'A4': 1, 'A5': 0, 'A6': -1, 'A7': 0, 'A8': -1, 'A9': 1, 'Lhash': '2167844358494010708769005296115', 'a10': [0.0, 0], 'a2': [-0.7071067811865476, 0], 'a3': [0.5773502691896257, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [-0.40824829046386296, 0], 'a7': [0.0, 0], 'a8': [-0.3535533905932738, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.949654024266134, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, -1]]], 'bad_primes': [2, 3], 'central_character': '93312.1', 'coefficient_field': '1.1.1.1', 'conductor': 93312, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1, 1], [1, -1], [1, 0, -2, 0, 25], [1, 0, 4, 0, 49], [1, 6, 31, 66, 121], [1, 0, 19, 0, 169], [1, 9, 52, 153, 289], [1, -1, 18, -19, 361], [1, 0, -2, 0, 529], [1, 0, -8, 0, 841], [1, 0, -26, 0, 961], [1, 0, 61, 0, 1369], [1, 3, 28, 123, 1681], [1, 2, 6, 86, 1849], [1, 0, -89, 0, 2209], [1, 0, -32, 0, 2809], [1, -6, 118, -354, 3481], [1, 0, 85, 0, 3721], [1, 11, 108, 737, 4489], [1, 0, 103, 0, 5041], [1, 26, 306, 1898, 5329], [1, 0, -32, 0, 6241], [1, -3, -14, -249, 6889], [1, -9, 142, -801, 7921], [1, -4, 117, -388, 9409], [1, 0, 136, 0, 10201], [1, 0, -62, 0, 10609], [1, 0, 178, 0, 11449], [1, 0, -38, 0, 11881], [1, 21, 334, 2373, 12769]], 'gamma_factors': [[], [0, 0]], 'index': 30, 'label': '4-93312-1.1-c1e2-0-30', 'load_key': 'Costa', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/2.0.8.1/1458.2/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0546875', 'prec': 30}, 'plot_values': [-1.1642714387423303e-74, 0.11369115718918721, 0.2282823527040329, 0.34461014894980696, 0.4633850816494883, 0.5851310367234689, 0.7101277051338789, 0.8383574709480923, 0.969458330264641, 1.102684693280774, 1.2368781587781474, 1.370450536294023, 1.5013814908978516, 1.627233163363385, 1.745183941237867, 1.852083195020853, 1.9445282267510813, 2.0189638941349877, 2.071804373034328, 2.099575320961477, 2.099073337699866, 2.0675381382164244, 2.002831328326425, 1.9036141935256679, 1.7695155797778535, 1.6012798769320984, 1.4008844316335258, 1.1716155363259104, 0.9180925733200049, 0.6462310271967552, 0.36313697432554104, 0.07692833426181162, -0.20351840566205853, -0.46889319052830747, -0.7098417134204072, -0.9174067226085099, -1.0835040433743461, -1.201411364162715, -1.2662437983070023, -1.2753872016922627, -1.2288585697755472, -1.1295628868721348, -0.9834178251122372, -0.7993218641195219, -0.5889477762814752, -0.3663519000743739, -0.14739994424673303, 0.05097820442610561, 0.211679658540855, 0.3184280847168294, 0.3568322406205782, 0.3154440601370032, 0.186749509193034, -0.031978323494271925, -0.3380338564476354, -0.7229058634061335, -1.172230444315831, -1.666108389364778, -2.1798050065067622, -2.6848266023117633, -3.1503415206055387, -3.544886576575112, -3.8382737663832476, -4.003589329087479, -4.0191596482398255, -3.870348017974204, -3.551044559110821, -3.0647196679529505, -2.424929795059108, -1.6551928164193275, -0.7881876915013301, 0.13572240845388112, 1.070595451168801, 1.9675463943428162, 2.7777683281905214, 3.455753109712646, 3.9624955554596872, 4.268448950924371, 4.355999738651382, 4.221247273770946, 3.874910678727127, 3.342237814701642, 2.6618584336906035, 1.8836004782785636, 1.065369848477271, 0.26927349241330495, -0.44276326395174775, -1.0135781801234556, -1.3952101535666201, -1.552841764411455, -1.4679123962061804, -1.1401148119044018, -0.5880615890636535, 0.15149627540250415, 1.0259046199027724, 1.9701823457059218, 2.911709318095903, 3.7756929666481915, 4.490999492891912, 4.995885515855154, 5.2431532152203175, 5.204279885014079, 4.872141138096806, 4.262051958617048, 3.4109839525514425, 2.3749699291102875, 1.2248654484164392, 0.040787011662594796, -1.094326035676882, -2.1014868999071843, -2.9121887685378414, -3.4741047198927704, -3.7554399680173725, -3.7475260287112957, -3.465398044185032, -2.946277203191436, -2.2460736361915377, -1.4342130656482206, -0.5872543189332923, 0.21811235106470803, 0.9120278494946824, 1.4377241403889514, 1.7564781076604221, 1.8507776611578246, 1.7253908427112, 1.4062357559347491, 0.9371704027416087, 0.37503435667983787, -0.21654383981372552, -0.7739285383663671, -1.2401379359985918, -1.5706832777980704, -1.7379700032073828, -1.7337967659403257, -1.5696930479726487, -1.2750720082742528, -0.8934167371322368, -0.4769383387063435, -0.08031798216440138, 0.24574843647189934, 0.4604586643751818, 0.5375808485819965, 0.4683540324118387, 0.26227336645640653, -0.05433053682035905, -0.44174589228210936, -0.8519493698952466, -1.2346732638407643, -1.5437246719585025, -1.7427723705297993, -1.8098740860007114, -1.7401649871348157, -1.5463513730549339, -1.2569258399517638, -0.9123088608802112, -0.5593908093530022, -0.24516340481767793, -0.010261482591099899, 0.11673438743488782, 0.12346345750267076, 0.015829378914938852, -0.18240157357735418, -0.4324598863715503, -0.6855759057195311, -0.8895187395861549, -0.9958398301746685, -0.9668694958628946, -0.7815163816826926, -0.4390477795966815, 0.039729216751040415, 0.6141377951708263, 1.2280314698748322, 1.8164323249206735, 2.3135978599756033, 2.6614863912753277, 2.8175013200247014, 2.7604528830334174, 2.4938800594022075, 2.04620307093279, 1.4675885947027032, 0.8238525236811111, 0.18813954148343798, -0.36855300537421964, -0.7867459603392944, -1.0264561831026573, -1.0726438707613517, -0.9373054728262804, -0.6578281865104779, -0.29173205882126135, 0.09156245548481069, 0.42086162352659084, 0.6338331608666891, 0.6866379133908557, 0.5611332361689516, 0.26851407119399073, -0.15127739072782606, -0.6344623344826792, -1.1021267514561612, -1.4716139424193826, -1.669069554861265, -1.6413618059487738, -1.3656040143160184, -0.854765009494242, -0.15834043497444536, 0.642284349953186, 1.443406894483778, 2.1324180771987944, 2.603349107329037, 2.772463326206432, 2.591688790666543, 2.0578824156166173, 1.2164045268654582, 0.1582078728538296, -0.9894849336089034, -2.077943926930962, -2.955363178425173, -3.48660587348521, -3.571630354718663, -3.1600446387689747, -2.25967705708763, -0.9378016172194678, 0.6853768543476613, 2.4503202288205137, 4.177187441908115, 5.687858469195191, 6.828044180358736, 7.48650254678143, 7.60872755007832, 7.2032020608413765, 6.3393154481979375, 5.137202461430545, 3.750898810908517, 2.3471659574209363, 1.0829704310824584, 0.08481312283855806, -0.5671472232096992, -0.8479161975178879, -0.7881954126215436, -0.46660578355637156, 0.005180435267449083, 0.5021136338218648, 0.9072232323836678, 1.1315406335198899, 1.1293785612056113, 0.906537669084089, 0.5200727969281386, 0.06953847655724993, -0.3190460213437361, -0.5141189519528502, -0.4011872496541585, 0.09639940216295831, 1.0018279322256782, 2.2769461739951957, 3.82358525289156, 5.4941489053974015, 7.110116994458381, 8.485870150731856], 'positive_zeros': ['1.71012766301984892032160078975656', '2.55542664503741642179895212945818', '2.89165547258907086481720434289005', '3.87488613206077017862725546028901', '4.66813422565207745216710594028157', '5.07562986357202465204427362014291', '5.85346497436345917136603741245316', '6.49242845094790160210673561056894', '6.97991898123414951150681433901469', '7.55904839014797635084846447901330', '7.86660308641488423632513423102641', '8.589031677461357649762066369538244', '8.755320776572624605657268556795751', '9.238097176676544541856919447608797'], 'prelabel': '4-93312-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.5617910437660596, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 812215071746209223, 'z1': {'__RealLiteral__': 0, 'data': '1.71012766301984892032160078975656', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.55542664503741642179895212945818', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.89165547258907086481720434289005', 'prec': 113}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.949654024266134, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 93312, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, -1, 1, 1, 0, -1, 0, -1, 1, 0, -6, 1, 0, 0, 0, 1, -9, -1, 1, 0, 0, 6, 0, -1, 2, 0, 1, 0, 0, 0, 0, -1, -6, 9, 0, 1, 0, -1, 0, 0, -3, 0, -2, -6, 0, 0, 0, 1, -4, -2, -9, 0, 0, -1, 0, 0, 1, 0, 6, 0, 0, 0, 0, 1, 0, 6, -11, -9, 0, 0, 0, -1, -26, 0, 2, 1, 0, 0, 0, 0, 1, 3, 3, 0, 0, 2, 0, 6, 9, 0, 0, 0, 0, 0, 0, -1, 4, 4, -6, 2], 'euler11': [1, 6, 31, 66, 121], 'euler13': [1, 0, 19, 0, 169], 'euler17': [1, 9, 52, 153, 289], 'euler19': [1, -1, 18, -19, 361], 'euler2': [1, 1, 0, 0, 0], 'euler23': [1, 0, -2, 0, 529], 'euler29': [1, 0, -8, 0, 841], 'euler3': [1, -1, 0, 0, 0], 'euler31': [1, 0, -26, 0, 961], 'euler37': [1, 0, 61, 0, 1369], 'euler41': [1, 3, 28, 123, 1681], 'euler43': [1, 2, 6, 86, 1849], 'euler47': [1, 0, -89, 0, 2209], 'euler5': [1, 0, -2, 0, 25], 'euler53': [1, 0, -32, 0, 2809], 'euler59': [1, -6, 118, -354, 3481], 'euler61': [1, 0, 85, 0, 3721], 'euler67': [1, 11, 108, 737, 4489], 'euler7': [1, 0, 4, 0, 49], 'euler71': [1, 0, 103, 0, 5041], 'euler73': [1, 26, 306, 1898, 5329], 'euler79': [1, 0, -32, 0, 6241], 'euler83': [1, -3, -14, -249, 6889], 'euler89': [1, -9, 142, -801, 7921], 'euler97': [1, -4, 117, -388, 9409], 'euler_factors': [[1, 1, 0, 0, 0], [1, -1, 0, 0, 0], [1, 0, -2, 0, 25], [1, 0, 4, 0, 49], [1, 6, 31, 66, 121], [1, 0, 19, 0, 169], [1, 9, 52, 153, 289], [1, -1, 18, -19, 361], [1, 0, -2, 0, 529], [1, 0, -8, 0, 841], [1, 0, -26, 0, 961], [1, 0, 61, 0, 1369], [1, 3, 28, 123, 1681], [1, 2, 6, 86, 1849], [1, 0, -89, 0, 2209], [1, 0, -32, 0, 2809], [1, -6, 118, -354, 3481], [1, 0, 85, 0, 3721], [1, 11, 108, 737, 4489], [1, 0, 103, 0, 5041], [1, 26, 306, 1898, 5329], [1, 0, -32, 0, 6241], [1, -3, -14, -249, 6889], [1, -9, 142, -801, 7921], [1, -4, 117, -388, 9409]], 'index': 30, 'instance_types': ['ECNF', 'BMF', 'ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.8.1/1458.6/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/1458.6/a', 'EllipticCurve/2.0.8.1/1458.2/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/1458.2/a'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-93312-1.1-c1e2-0-30', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'prelabel': '4-93312-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.5617910437660596, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 812215071746209223, 'z1': {'__RealLiteral__': 0, 'data': '1.71012766301984892032160078975656', 'prec': 113}}
-
lfunc_instances • Show schema
Hide schema
-
id: 9821273
{'Lhash': '2167844358494010708769005296115', 'Lhash_array': ['2167844358494010708769005296115'], 'label': '4-93312-1.1-c1e2-0-30', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/1458.2/a'}
-
id: 9821254
{'Lhash': '2167844358494010708769005296115', 'Lhash_array': ['2167844358494010708769005296115'], 'label': '4-93312-1.1-c1e2-0-30', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/1458.2/a'}
-
id: 9820840
{'Lhash': '2167844358494010708769005296115', 'Lhash_array': ['2167844358494010708769005296115'], 'label': '4-93312-1.1-c1e2-0-30', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/1458.6/a'}
-
id: 9820470
{'Lhash': '2167844358494010708769005296115', 'Lhash_array': ['2167844358494010708769005296115'], 'label': '4-93312-1.1-c1e2-0-30', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/1458.6/a'}