-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2211217205960162049430157812985', 'a10': [-1.9824860220569813, 1.0404889300099291], 'a2': [-0.9117565466482231, 0.3457836478924826], 'a3': [0.5680647467311558, -0.8229838658936564], 'a4': [-0.785287827136141, 0.6957043071018402], 'a5': [2.2793200213826, -0.27675955739448055], 'a6': [-0.23336238844682994, 0.9467884278782229], 'a7': [1.7819416170541784, -3.3952060863327116], 'a8': [1.381753350460146, -2.632711049786469], 'a9': [-0.3546048870425356, -0.9350162426854148], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.048415382478917, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.5680647467311558, 0.8229838658936564]]], [13, [[1.0, 0], [1.2076655835391872, -3.3972847743948336]]]], 'bad_primes': [3, 13], 'central_character': '507.142', 'coefficient_field': 'CDF', 'conductor': 507, 'conductor_radical': 39, 'conjugate': '1174792471099734684655099860764', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9117565466482231, -0.3457836478924826], [1.4970214963422022, -1.3262453164815904]], [[1.0, 0], [-0.5680647467311558, 0.8229838658936564]], [[1.0, 0], [-2.2793200213826, 0.27675955739448055], [4.85470908713026, -1.1965783214377888]], [[1.0, 0], [-1.7819416170541784, 3.3952060863327116], [-3.976453227118091, -5.760887061255595]], [[1.0, 0], [0.05394663291714625, 0.02045925920705739], [8.233618229882111, 7.294349240648748]], [[1.0, 0], [1.2076655835391872, -3.3972847743948336]], [[1.0, 0], [4.907592660537823, 2.5757033237436944], [9.657100694429648, 13.99072572019216]], [[1.0, 0], [0, 6.274855572348264], [-19.0, 0]], [[1.0, 0], [-3.5159584672195914, 0], [23.0, 0]], [[1.0, 0], [-2.7509984971080375, -7.253786883345], [-21.706811696961932, 19.230557088983062]], [[1.0, 0], [-1.7000674455101796, 6.897444762776187], [-27.44913679524951, -14.406418333356825]], [[1.0, 0], [-1.9230101003252495, 7.8019586695124925], [-32.76187294916877, -17.194757365619438]], [[1.0, 0], [-8.265658343774607, -5.705372010572703], [14.53880036874396, 38.335665950102005]], [[1.0, 0], [1.6222468971628126, -0.39984794852294625], [38.07460910308802, -19.983096397882047]], [[1.0, 0], [-2.419264498911422, 2.730785108305578], [-5.665223972000184, -46.657317082608536]], [[1.0, 0], [3.0312445068393483, 1.5909198442908854], [30.107431576751257, 43.61814489236379]], [[1.0, 0], [3.8322408625955995, -0.4653182857217441], [57.28556722813707, -14.119624192965908]], [[1.0, 0], [-10.998168741306259, 5.772284242305486], [34.651949550600506, -50.20201581951304]], [[1.0, 0], [2.3916461310176107, -2.6996104154210006], [-8.075957577106644, -66.51149456456962]], [[1.0, 0], [-7.117870135943986, -4.913111014211251], [25.17694698002003, 66.38615323066445]], [[1.0, 0], [9.893743259172968, 3.752201887713373], [54.64128461649038, 48.40795405157805]], [[1.0, 0], [-10.550882130333646, -9.347265917219433], [9.522397740170522, 78.42400105374627]], [[1.0, 0], [2.755507978571419, -1.9019898285164154], [29.432205624530457, -77.60634814288943]], [[1.0, 0], [0, -15.479371966373947], [-89.0, 0]], [[1.0, 0], [-3.4510874606303923, -0.4190378837432172], [94.18135629032705, 23.213619435893104]], [[1.0, 0], [1.9774696442020736, -0.48740249211353204], [89.4310585909742, -46.937040376420626]], [[1.0, 0], [8.261098428415071, -11.968267279861045], [-36.52430336538117, -96.30667299659773]], [[1.0, 0], [-1.2697100672233552, -10.457003200970423], [-103.89077446458757, 25.606776078768682]], [[1.0, 0], [-0.7173286462392392, -2.910316721409478], [-96.51470679619987, 50.65482575277077]], [[1.0, 0], [5.731109588786295, 8.302945663114256], [-40.070352235806524, 105.65683542345188]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 21, 'label': '2-507-169.142-c1-0-21', '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/507/2/p/a/142/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.2030504207781452, 1.294348796694722, 1.3787382076552621, 1.4536466479647165, 1.5135427509817254, 1.550703832693932, 1.556292212370977, 1.5215738333771014, 1.4391786440999652, 1.3043401119917803, 1.1160510445776473, 0.8780503465668712, 0.5995297346192223, 0.2954344763963682, -0.01376424857267933, -0.3029220724911437, -0.5437474973311756, -0.7069806011579206, -0.7651196024504482, -0.6954996238548871, -0.48344153292138903, -0.1251197525582448, 0.3702400010434742, 0.9792167842690849, 1.6644307835016485, 2.3763742091824183, 3.0568880137058057, 3.644134658838751, 4.078698817615493, 4.310239874754898, 4.303953938501965, 4.04601024480752, 3.547133793397937, 2.84362922460511, 1.9953822239791676, 1.0807185025170887, 0.18841275219548875, -0.5924291509389793, -1.1835031724406675, -1.5280625970680102, -1.5997867945023876, -1.40834360187225, -1.000535891169843, -0.45643613059017973, 0.11942341952886444, 0.6110064399675844, 0.9063836110171394, 0.9139680371428769, 0.5770585360812786, -0.11558222125852821, -1.1249860231403674, -2.364211771539151, -3.707709899921725, -5.0068837789057135, -6.109878095979444, -6.882822556369504, -7.229345884449073, -7.1052531490227375, -6.525856781094099, -5.564508172866633, -4.342246189348135, -3.0099468443857362, -1.7256746237841483, -0.6308571035371734, 0.1707603919769245, 0.6277727075187306, 0.7467910006540553, 0.5880732527542749, 0.2518389532663322, -0.14226773499270504, -0.4787600703783436, -0.6684605447021272, -0.6649176650845636, -0.4718064520159045, -0.1397509458894156, 0.24688464050306702, 0.5905990980745466, 0.8044725974297207, 0.833893992739092, 0.6714003821317794, 0.36099792229590943, -0.009548047656144672, -0.3273917026027956, -0.48068825757337236, -0.3866251994683102, -0.015133653236504842, 0.5974810497271545, 1.348932659365329, 2.0864907982298315, 2.6354992672770914, 2.8356633699871794, 2.5777645410375816, 1.8327908270312208, 0.6665165924698943, -0.764782086033247, -2.2379996887468674, -3.5026151111465915, -4.328548207608522, -4.552866613849953, -4.1154126123858115, -3.075236067108451, -1.6034183479096504, 0.04725752300660847, 1.5903117639406454, 2.761705367858771, 3.372423829996513, 3.346173713514466, 2.733749118839117, 1.7005156114931006, 0.4893269220055828, -0.6332627478216307, -1.4356853796166495, -1.7717725906392776, -1.6113464537567357, -1.043781911974253, -0.2534797634923648, 0.5272480651599873, 1.0769361646011857, 1.241428839620487, 0.9743642928815776, 0.35153736385524603, -0.4449193280272115, -1.169366152672042, -1.572673658917637, -1.4651600298276415, -0.7671104137215857, 0.46580229217487407, 2.049036315353328, 3.706815690777699, 5.1324183031274995, 6.056943064244709, 6.310068708800499, 5.858058455004534, 4.809710532884665, 3.388804192848725, 1.8798997245434297, 0.5610118082866173, -0.3600421686551028, -0.7898071100917157, -0.7631205359521541, -0.4239306752995216, 0.02122758921746615, 0.364177648296004, 0.45380954926216593, 0.23661438971627424, -0.23185543047580764, -0.8074566790927208, -1.3038201426588147, -1.5512665653461881, -1.4512614138816622, -1.0104567855412319, -0.3439599887357429, 0.35388146914212937, 0.8635504469600599, 1.0042638700260953, 0.6893961037921545, -0.04301883670779155, -1.0344875620834457, -2.0450513081298394, -2.817127618964907, -3.146745160025011, -2.941988018447032, -2.251471067915928, -1.2537423171965218, -0.20949612123112388, 0.6106975712071577, 1.0029368415961655, 0.8887083264958923, 0.33818305306129776, -0.4497130467867903, -1.205812280806425, -1.671621114894171, -1.6792446719941152, -1.20633167342188, -0.3885212821059594, 0.5162067743111706, 1.2027906401726611, 1.4132706179007635, 1.0225881936772854, 0.08981852471690047, -1.1424531334575636, -2.303523134100983, -2.9917581570129173, -2.887803114847191, -1.8521622731676475, 0.02144171706017015, 2.414109047975401, 4.851612151725793, 6.819012337005522, 7.889894369697151, 7.8352039690619755, 6.681658260106501, 4.703315059411957, 2.348372435314237, 0.1213702668066096, -1.5465527114962876, -2.403497127038635, -2.429968289526297, -1.8259382810974953, -0.937497857608322, -0.14608194651425746, 0.2463857618463275, 0.10269126120575946, -0.5182359776697596, -1.391076491368791, -2.203845093296678, -2.6614604896923355, -2.580380485326526, -1.9450888478530797, -0.9097967283883609, 0.25370455604797615, 1.2440985875510822, 1.8255017659817312, 1.8986660080207882, 1.5259875320570473, 0.9032667607018589, 0.2886912569703038, -0.08653989837766518, -0.09573606419717795, 0.24356532152447846, 0.780683895098718, 1.2893614215164437, 1.551550763410155, 1.4380311737464981, 0.9572889442233863, 0.25479415833621805, -0.4381114345420928, -0.8887353757664593, -0.9516266864795406, -0.6293664245587943, -0.08216740764509163, 0.4201306924348309, 0.5901329236835449, 0.2292956707377984, -0.687786487107281, -1.9822047450735674, -3.3073233042667938, -4.245619265405786, -4.437504654035827, -3.7015552933811273, -2.1062186624594537, 0.03299267724084676, 2.2336880008539017, 3.9820235906635877, 4.882535319605482, 4.7755579705090945, 3.784492481588804, 2.2767867072301025, 0.7498546659473116, -0.3225767942980827, -0.6350771280506625, -0.13999989438782226, 0.9465922920486018, 2.22387245673267, 3.243592719579986, 3.6601496805625247, 3.3435500708346035], 'positive_zeros': ['1.74434280673400993510686248701981', '2.65986402454920301192227468788694', '4.52812008040512289362533916902800', '5.47340818453363428179015288452187', '6.10778845790477044548611274915530', '7.968465693497641748204455840649415', '8.579574891669162829524885053472581', '9.295579258993439157169738893035274', '10.12172601321466082275951465264724', '10.62872720532705546412768816240715'], 'prelabel': '2-507-169.142-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0120674398436345, 'root_angle': 0.3002765087705261, 'root_number': '0.5870822554074578 + 0.8095272851397243*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.150138254385', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.74434280673400993510686248702', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.65986402454920301192227468789', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.52812008040512289362533916903', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.048415382478917, 'bad_primes': [3, 13], 'central_character': '169.142', 'conductor': 507, 'conductor_radical': 39, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/507/2/p/a/142/5'], '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': '2-507-169.142-c1-0-21', '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': '2-507-169.142-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0120674398436345, 'root_angle': 0.15013825438526304, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.74434280673400993510686248702', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2211217205960162049430157812985', 'Lhash_array': ['2211217205960162049430157812985'], 'label': '2-507-169.142-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/507/2/p/a/142/5'}