-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3864981155923801717504895815022', 'a10': [0.79128784747792, 0.0], 'a2': [0.0, -1.0], 'a3': [1.79128784747792, 0.0], 'a4': [-1.0, 0.0], 'a5': [0.0, 0.79128784747792], 'a6': [0.0, -1.79128784747792], 'a7': [-2.0, 0.0], 'a8': [0.0, 1.0], 'a9': [0.20871215252208, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.0]]], [37, [[1.0, 0], [-4.0, 4.58257569495584]]]], 'bad_primes': [2, 37], 'central_character': '74.73', 'coefficient_field': 'CDF', 'conductor': 74, 'conductor_radical': 74, 'conjugate': '3327703455453820779328774272632', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0]], [[1.0, 0], [-1.79128784747792, 0], [3.0, 0]], [[1.0, 0], [0, -0.79128784747792], [-5.0, 0]], [[1.0, 0], [2.0, 0], [7.0, 0]], [[1.0, 0], [0.79128784747792, 0], [11.0, 0]], [[1.0, 0], [0, 3.79128784747792], [-13.0, 0]], [[1.0, 0], [0, -7.58257569495584], [-17.0, 0]], [[1.0, 0], [0, -1.58257569495584], [-19.0, 0]], [[1.0, 0], [0, 3.79128784747792], [-23.0, 0]], [[1.0, 0], [0, -3.79128784747792], [-29.0, 0]], [[1.0, 0], [0, 8.37386354243376], [-31.0, 0]], [[1.0, 0], [-4.0, 4.58257569495584]], [[1.0, 0], [-9.79128784747792, 0], [41.0, 0]], [[1.0, 0], [0, 6.0], [-43.0, 0]], [[1.0, 0], [7.58257569495584, 0], [47.0, 0]], [[1.0, 0], [1.58257569495584, 0], [53.0, 0]], [[1.0, 0], [0, -1.58257569495584], [-59.0, 0]], [[1.0, 0], [0, -12.79128784747792], [-61.0, 0]], [[1.0, 0], [-6.37386354243376, 0], [67.0, 0]], [[1.0, 0], [9.16515138991168, 0], [71.0, 0]], [[1.0, 0], [4.37386354243376, 0], [73.0, 0]], [[1.0, 0], [0, -8.20871215252208], [-79.0, 0]], [[1.0, 0], [-15.16515138991168, 0], [83.0, 0]], [[1.0, 0], [0, -6.0], [-89.0, 0]], [[1.0, 0], [0, 13.58257569495584], [-97.0, 0]], [[1.0, 0], [-7.58257569495584, 0], [101.0, 0]], [[1.0, 0], [0, -6.79128784747792], [-103.0, 0]], [[1.0, 0], [5.37386354243376, 0], [107.0, 0]], [[1.0, 0], [0, -6.0], [-109.0, 0]], [[1.0, 0], [0, 10.41742430504416], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-74-37.36-c1-0-2', '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/74/2/b/a/73/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.0796807517164104, 1.1081212105026697, 1.1530604988646265, 1.2139640158918077, 1.2893855056690935, 1.3771319121932426, 1.474409802749904, 1.5779205732703396, 1.683907716169294, 1.7881786378624536, 1.886126890187902, 1.9727760023361536, 2.042859401761176, 2.0909448212325197, 2.111606577249934, 2.099644834051226, 2.050347008222511, 1.9597825561328515, 1.8251184575441703, 1.644938872426296, 1.419548939716253, 1.1512398274922198, 0.8444903023604899, 0.5060796404962807, 0.1450880034567202, -0.2272362719788794, -0.5977575021500157, -0.951888910226878, -1.2741818545411976, -1.5490541758917242, -1.761631364857196, -1.8986615907046347, -1.9494537630150173, -1.9067778485206848, -1.7676598206723377, -1.5340010091296188, -1.212954205763117, -0.8169973499282075, -0.36366022970618994, 0.1251198388558903, 0.6240117702138507, 1.105643021615613, 1.5422285950470238, 1.9073846866294804, 2.1780083786312994, 2.3360847482738105, 2.3702720605578174, 2.277116640152667, 2.061763146372425, 1.738053840909994, 1.3279513285233833, 0.8602710844388696, 0.3687694069674744, -0.11030542884736179, -0.541031701036987, -0.8907848987412792, -1.1331074486482131, -1.2502092114520806, -1.2348394472973048, -1.0913061843894654, -0.835479949990813, -0.4937024554890313, -0.1006211251592607, 0.3039211049425502, 0.6787048390806936, 0.9853332189381075, 1.1924136053249146, 1.279290907914994, 1.2389096310441745, 1.0794352596808903, 0.8243636076100098, 0.5109831687831926, 0.1872194122864041, -0.09293384694654874, -0.2750205759523235, -0.3102457756618279, -0.16149448357296728, 0.1914163758613773, 0.7478879585110197, 1.4846246265504892, 2.3560179429645762, 3.296968457987425, 4.2280250869974445, 5.062455193369376, 5.714614362893986, 6.108793465554246, 6.187608546200856, 5.918985836448626, 5.3008890485170275, 4.3631361998132325, 3.1659426905311907, 1.795178274239359, 0.3547003077504839, -1.0435191696081718, -2.2904636397360574, -3.291142765972809, -3.9744116652547175, -4.3003797887918545, -4.26448844460222, -3.8976979972497263, -3.262673344744163, -2.4463375965586702, -1.5496195996728608, -0.675591462314639, 0.08257448823705002, 0.6523407431497049, 0.98987403522697, 1.0844040502478516, 0.9582869820050576, 0.6627430339685927, 0.2698125991402901, -0.13840394895784203, -0.48176694500998685, -0.6937204567813747, -0.7308820130232098, -0.5792166783346475, -0.25587063276591165, 0.19365594090783678, 0.7026462146834509, 1.1936219083784405, 1.590605741601555, 1.8313677373072885, 1.8777796075724973, 1.7226286002370277, 1.3917269463128772, 0.9408336282440567, 0.4476870547805571, 0.0002156897913563042, -0.31736967819599754, -0.43849768060049393, -0.325976145510523, 0.020399805005170166, 0.5617590687459002, 1.2241679607254081, 1.908394675851333, 2.504152031235154, 2.906781751253645, 3.033865829156503, 2.8391485412636013, 2.321460806254992, 1.5270273567745656, 0.5445147883341938, -0.5066978312313085, -1.4934478850152026, -2.28844848442844, -2.7896756791978152, -2.936408359026399, -2.719265591252221, -2.182452426393824, -1.4176160682877796, -0.5500490987012904, 0.2807574686202561, 0.9432221057718733, 1.3349198305633028, 1.399474265324707, 1.136206468945163, 0.6007586133974954, -0.1036477099379396, -0.8431098898211936, -1.47549051169921, -1.8747921857944725, -1.9534064094261323, -1.6784162930999253, -1.0790217145687309, -0.24357076949486867, 0.6935995369021307, 1.5735709225245795, 2.2390948564335775, 2.5613570569310076, 2.462714934304186, 1.9314305170784425, 1.0256849735408042, -0.1340727525355713, -1.3834134351477285, -2.539971632543733, -3.43297082619674, -3.9312683980304763, -3.9651221406758066, -3.537883660909545, -2.7255109450771493, -1.6638790973885096, -0.5259927292880716, 0.507012069504652, 1.2760692138961718, 1.6703394689653477, 1.6447691459767038, 1.2260159410557885, 0.5057857148929792, -0.3771102526513178, -1.2626289594929334, -1.9985186501359653, -2.4671549864601983, -2.6052913123976937, -2.4131798624352276, -1.9515480254102098, -1.327232716647807, -0.6704448708499519, -0.10823508437843177, 0.2605559354173579, 0.38390121487714296, 0.2650914652097725, -0.040470852921109156, -0.4394131972676628, -0.8224455516224836, -1.0896390157943963, -1.1735242721063146, -1.0549887448174686, -0.7683889019385991, -0.3945149443376855, -0.04261140851449746, 0.1749530549095085, 0.17006283267809574, -0.09767646783463685, -0.606753794982105, -1.2724878110385383, -1.9597354217878147, -2.507707768716273, -2.7623629723689995, -2.6100001834936464, -2.0050736511862177, -0.9860590195277161, 0.32466778282063236, 1.7379157361608797, 3.0292948355594898, 3.979856618707456, 4.418158068417921, 4.255499576473043, 3.507075819645116, 2.2942662887738217, 0.8268322996814047, -0.6322981332675289, -1.8134641997599223, -2.489342649603122, -2.517320741616815, -1.866920366828256, -0.6267673644712853, 1.010505289149404, 2.7827480103288655, 4.405690058562415, 5.624180582776838, 6.257429496027975, 6.229581630863526, 5.579882791060557, 4.45078471730464, 3.0567571716809256, 1.6404207938509288, 0.42508691461689013, -0.42662633637556824, -0.8398615104469527, -0.8351730114107143, -0.5158469030002516, -0.03831093552155173, 0.4273849386363046, 0.7380228911534266, 0.8095766437547944, 0.6343960819108658, 0.2796423046029178], 'positive_zeros': ['3.04893253332420279706449546079034', '4.84351231959469134717944299118268', '6.59542030368139108942676692191673', '7.78092525267977142108962169786429', '9.079728672022026253730412723330957', '9.566375257743002105551904355024597', '11.53096802022679387544575129822110', '12.98493668412561973418339308322415', '13.83156345533807426231772609099838', '14.57429349606826310858075089622765'], 'prelabel': '2-74-37.36-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7686956321961738, 'root_angle': 0.2284265717541327, 'root_number': '0.7533708035008839 + 0.6575959492214292*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.114213285877', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.04893253332420279706449546079', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.84351231959469134717944299118', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.59542030368139108942676692192', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'bad_primes': [2, 37], 'central_character': '37.36', 'conductor': 74, 'conductor_radical': 74, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/74/2/b/a/73/2'], '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': '2-74-37.36-c1-0-2', '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': '2-74-37.36-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7686956321961738, 'root_angle': 0.11421328587706635, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.04893253332420279706449546079', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3864981155923801717504895815022', 'Lhash_array': ['3864981155923801717504895815022'], 'label': '2-74-37.36-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/74/2/b/a/73/2'}