-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1325993633428652206414066863469', 'a10': [0.012774427683235733, 0.0], 'a2': [-0.7762440417546174, 0.0], 'a3': [3.0100825035661822, 0.0], 'a4': [-1.3974451876404559, 0.0], 'a5': [-0.01645671592449263, 0.0], 'a6': [-2.3365586085830707, 0.0], 'a7': [-0.7937215604523543, 0.0], 'a8': [2.637246584093802, 0.0], 'a9': [6.060596678275256, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.84418973575603, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [11, 13], 'central_character': '1859.1', 'coefficient_field': 'CDF', 'conductor': 1859, 'conductor_radical': 143, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7762440417546174, 0], [2.0, 0]], [[1.0, 0], [-3.0100825035661822, 0], [3.0, 0]], [[1.0, 0], [0.01645671592449263, 0], [5.0, 0]], [[1.0, 0], [0.7937215604523543, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.1283415708488915, 0], [17.0, 0]], [[1.0, 0], [1.225956151080095, 0], [19.0, 0]], [[1.0, 0], [-4.269253477190354, 0], [23.0, 0]], [[1.0, 0], [-8.019476690030036, 0], [29.0, 0]], [[1.0, 0], [2.4936363416320058, 0], [31.0, 0]], [[1.0, 0], [-8.886742403342767, 0], [37.0, 0]], [[1.0, 0], [-8.43142401420267, 0], [41.0, 0]], [[1.0, 0], [-11.895426974777425, 0], [43.0, 0]], [[1.0, 0], [12.275299479929513, 0], [47.0, 0]], [[1.0, 0], [-4.566751595087621, 0], [53.0, 0]], [[1.0, 0], [0.265213545757961, 0], [59.0, 0]], [[1.0, 0], [4.492395303148909, 0], [61.0, 0]], [[1.0, 0], [5.314105763172414, 0], [67.0, 0]], [[1.0, 0], [-13.116210089790995, 0], [71.0, 0]], [[1.0, 0], [-11.543448289307719, 0], [73.0, 0]], [[1.0, 0], [9.35606066087677, 0], [79.0, 0]], [[1.0, 0], [-4.816474407189733, 0], [83.0, 0]], [[1.0, 0], [-1.6616419835461678, 0], [89.0, 0]], [[1.0, 0], [8.352824735724173, 0], [97.0, 0]], [[1.0, 0], [-5.6723467957094025, 0], [101.0, 0]], [[1.0, 0], [-16.922537463267226, 0], [103.0, 0]], [[1.0, 0], [-4.360322445676904, 0], [107.0, 0]], [[1.0, 0], [-17.49351297321354, 0], [109.0, 0]], [[1.0, 0], [-1.1770869498009202, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 50, 'label': '2-1859-1.1-c1-0-50', 'leading_term': '2.0915428057374249669039370596931', '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/1859/2/a/s/1/9', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.091542805737425, 2.086288707422115, 2.0703961273045937, 2.0434852098009593, 2.004958640578697, 1.9540523480159866, 1.8899010248183687, 1.8116139756790526, 1.7183566030189374, 1.6094330793822182, 1.4843662645383324, 1.3429715472345398, 1.1854219011551184, 1.0123019695812452, 0.8246494108403762, 0.6239820604948282, 0.412309729954116, 0.1921297044716783, -0.03359473749252615, -0.2614731592436891, -0.4877441682670683, -0.7083485698442631, -0.9190185624135812, -1.115381518936246, -1.2930763163746346, -1.4478795795267918, -1.5758386217332712, -1.6734073216561303, -1.7375807019305678, -1.7660236015111521, -1.7571885872164, -1.7104181569947752, -1.6260263695953425, -1.5053553092682799, -1.3508022701070488, -1.1658142254743626, -0.9548470280709103, -0.72328785105859, -0.4773406063734215, -0.22387542982339775, 0.029755238184187377, 0.27592997227312, 0.5069956234435602, 0.7155216906727473, 0.8945637442305618, 1.0379268248782147, 1.1404189970206189, 1.1980848147817877, 1.2084084150714642, 1.1704763166997296, 1.0850908009636853, 0.954825981854643, 0.7840203297937525, 0.5787014588446998, 0.3464413711310403, 0.09614300188189583, -0.1622382655161099, -0.418031547977603, -0.6602364571832352, -0.8779460427890968, -1.0607922068294888, -1.1993971566541937, -1.2858130511636796, -1.3139312280265911, -1.2798423607065021, -1.1821296405358792, -1.0220786374270967, -0.8037898557255881, -0.5341831253704032, -0.22288677179280475, 0.11799112680769155, 0.4742073106203189, 0.8298366488874477, 1.1678220718083974, 1.4706041717558953, 1.7208091108483885, 1.9019697070614188, 1.999251661853966, 2.000155023379646, 1.8951603001834525, 1.6782892556310545, 1.347552375326629, 0.9052583019581327, 0.35816510564822807, -0.2825410287914697, -1.0014474559676807, -1.7792974645518616, -2.593546049339287, -3.4190738636733706, -4.229036603626269, -4.995820166814664, -5.69206601368915, -6.29172656019225, -6.771107425433884, -7.109852163025014, -7.291825861469872, -7.30585676303763, -7.146299783912179, -6.81339238676554, -6.313381430937778, -5.658409087442015, -4.866156261251978, -3.959252755710977, -2.964474145902372, -1.9117554834164334, -0.833061024699797, 0.23884331773994708, 1.2716625761428233, 2.234834946970345, 3.1007275386202386, 3.845711565204199, 4.451067561737513, 4.903678352053114, 5.196476871844494, 5.328627129143484, 5.305429060341821, 5.137951214899596, 4.842408424021378, 4.439314202728241, 3.952448937948473, 3.407694312550183, 2.8317913744675645, 2.2510837634287975, 1.6903085784447351, 1.1714950911580486, 0.7130260399246321, 0.3289078087637004, 0.0282848037318593, -0.18477966230305728, -0.3112480010216443, -0.3567854228414412, -0.3311910314067273, -0.247618091259824, -0.12163033845603029, 0.029849633990912235, 0.18963784317383442, 0.3413676440595873, 0.4704863342949263, 0.5651111810337331, 0.6166948386913672, 0.6204616087991316, 0.575589904645915, 0.4851318345733273, 0.35567710096786925, 0.1967844523986736, 0.020218738930196368, -0.16095573049499742, -0.3333651727370471, -0.4843333026792593, -0.6028370567159265, -0.6803452822350213, -0.7114813434364501, -0.6944612962940233, -0.6312733782852358, -0.5275812338044905, -0.3923515575293742, -0.23722555668079498, -0.07567161462783434, 0.07802740435406176, 0.2098857401640605, 0.30734968966779136, 0.36037605386809163, 0.36237500617697893, 0.3109443937394992, 0.20833365231504053, 0.061591229784229894, -0.11763117713752927, -0.31362228608067294, -0.5074842816266579, -0.6782937454813587, -0.8044876794422473, -0.865393745783917, -0.8428102471534936, -0.7225333213650282, -0.49572708728917175, -0.16003742115855413, 0.2796383728792937, 0.8107959784552481, 1.4134295084646487, 2.0606178462238045, 2.7195822382001538, 3.353175298957672, 3.9217326272280997, 4.385192392353275, 4.705367296883722, 4.848238771256693, 4.7861362741224305, 4.49966587973338, 3.9792621510357793, 3.226255307507477, 2.25337105055728, 1.0846117594991969, -0.24549665627212974, -1.6932702691123085, -3.2077855163026134, -4.733255993020575, -6.2117430404819824, -7.5860522087520845, -8.802652867366312, -9.814453085209799, -10.583266972873123, -11.081826904964268, -11.295217692909286, -11.221642513725998, -10.872469318446822, -10.271549204657397, -9.453842200358046, -8.46342829600903, -7.351019647635606, -6.171121150693046, -4.979008941566034, -3.8277082536871148, -2.7651525291839167, -1.8316945877779944, -1.0581185641054112, -0.46426955917373425, -0.058378488454123745, 0.16288503437448562, 0.21364586445345818, 0.1174027470464033, -0.09494357120967466, -0.3874756118451236, -0.7218935634616555, -1.0602192467516804, -1.3673868904718605, -1.6135471836596924, -1.7759321447750005, -1.8401598971441415, -1.800898339793511, -1.6618522274185612, -1.4350861747188985, -1.139743223138056, -0.8002615225046608, -0.4442273179236926, -0.10002820797386397, 0.2055153580294519, 0.4493612400617079, 0.6141322323930756, 0.6895351640327403, 0.673204326500867, 0.5709041165346431, 0.39607394004180435, 0.16874822004316042, -0.08606786676292727, -0.34044408838388107, -0.5658360100296504, -0.7354826416247374, -0.8267036082963211, -0.8229136776122854, -0.7151914301125009, -0.5032704568529986, -0.19586354636111794, 0.1897200969493364, 0.6286510723377646, 1.0902824605503791, 1.5403625877276983, 1.94359995612573], 'positive_zeros': ['1.04602453798382507937057180976916', '2.33682064660647311484667660058985', '3.24454634110249998393006527189396', '4.08170550512725666942254944894584', '4.89699993907720020788983686784237', '6.19775712498467604773597387346035', '7.44797875457810097477987842510482', '7.84046354248518948446845093759369', '8.502626826863905738482539098381208', '9.227356833363515596045933276796054'], 'prelabel': '2-1859-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8528158190803814, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.04602453798382507937057180977', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.33682064660647311484667660059', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.24454634110249998393006527189', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 14.84418973575603, 'bad_primes': [11, 13], 'central_character': '1.1', 'conductor': 1859, 'conductor_radical': 143, 'degree': 2, 'index': 50, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1859/2/a/s/1/9'], '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': '2-1859-1.1-c1-0-50', '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': '2-1859-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8528158190803814, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.04602453798382507937057180977', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1325993633428652206414066863469', 'Lhash_array': ['1325993633428652206414066863469'], 'label': '2-1859-1.1-c1-0-50', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1859/2/a/s/1/9'}