-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1081106035049366566222365666583', 'a10': [4.400807790603425, 1.3336825557896363e-60], 'a2': [1.0625143657319702, -1.8403288652195924], 'a3': [0.0, 0.0], 'a4': [-1.2578735547736217, -2.178700906365186], 'a5': [1.035470185754075, 1.7934869714488406], 'a6': [0.0, 0.0], 'a7': [-2.4243363738191146, 4.199073774092001], 'a8': [-1.095977425957373, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.487', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '2542443607289547879294943784758', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0625143657319702, 1.8403288652195924], [-1.0, -1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.035470185754075, -1.7934869714488406], [-2.5, 4.330127018922194]], [[1.0, 0], [2.4243363738191146, -4.199073774092001], [-3.5, -6.06217782649107]], [[1.0, 0], [2.0747444306134684, -3.5935627665430885], [-5.5, -9.526279441628825]], [[1.0, 0], [-0.6080076298496646, -1.0531001062891505], [-6.5, 11.258330249197702]], [[1.0, 0], [-2.3636381320245734, 0], [17.0, 0]], [[1.0, 0], [1.8380064104318812, 0], [19.0, 0]], [[1.0, 0], [-2.1517844490987224, -3.726999992775594], [-11.5, 19.91858428704209]], [[1.0, 0], [1.4909099160872268, -2.582331724171328], [-14.5, -25.11473670974872]], [[1.0, 0], [0.7367932766232042, 1.2761633897865399], [-15.5, 26.846787517317598]], [[1.0, 0], [-8.971081362806435, 0], [37.0, 0]], [[1.0, 0], [1.1302622209983224, 1.9576715926447372], [-20.5, 35.50704155516198]], [[1.0, 0], [-2.742428706452921, 4.750025855711853], [-21.5, -37.239092362730865]], [[1.0, 0], [3.5915656712385378, -6.2207742213053665], [-23.5, -40.703193977868615]], [[1.0, 0], [6.328029027960441, 0], [53.0, 0]], [[1.0, 0], [0.13112837844104466, 0.22712101377400878], [-29.5, 51.09549882328188]], [[1.0, 0], [-2.227802871779223, 3.858667763169467], [-30.5, -52.827549630850754]], [[1.0, 0], [2.0655519464633585, 3.5776409169473267], [-33.5, 58.023702053557386]], [[1.0, 0], [-3.0855104468886085, 0], [71.0, 0]], [[1.0, 0], [-12.760062443166179, 0], [73.0, 0]], [[1.0, 0], [2.276203266632224, -3.9424997061612603], [-39.5, -68.41600689897065]], [[1.0, 0], [-4.22652887971219, 7.320562759318682], [-41.5, -71.88010851410841]], [[1.0, 0], [-16.963167810208827, 0], [89.0, 0]], [[1.0, 0], [-2.5548856092570102, 4.425191682759708], [-48.5, -84.00446416709055]], [[1.0, 0], [9.289940173814173, -16.090648380321394], [-50.5, -87.4685657822283]], [[1.0, 0], [4.5028848635379015, 7.799225364280496], [-51.5, 89.20061658979718]], [[1.0, 0], [-7.426803772921361, 0], [107.0, 0]], [[1.0, 0], [5.623962210180389, 0], [109.0, 0]], [[1.0, 0], [-1.2013341685840142, -2.0807718168560276], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-3e6-9.7-c1-0-6', '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/729/2/c/d/487/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.0588197452212076, 1.9059460801980455, 1.7238798437336593, 1.4997006903469947, 1.2183599391338125, 0.8651072243450966, 0.42790223815427814, -0.1004126178920636, -0.7202827452788937, -1.4240307033995838, -2.1949677683827087, -3.007164762331501, -3.826026751472918, -4.609784953201055, -5.311948905979758, -5.884659449955536, -6.282759910813681, -6.468274537137311, -6.414868186944743, -6.111779420120368, -5.566689542595671, -4.807027889492513, -3.879326805658346, -2.846426623361495, -1.7825780330330308, -0.7667712395034072, 0.12509744021241215, 0.8283725141222169, 1.297098350514986, 1.5097594389157687, 1.4723882769484578, 1.2183953333037634, 0.804874621500379, 0.3056242272254808, -0.19837178536709257, -0.6298041145430539, -0.9257342824851778, -1.0465142579481421, -0.9814632273015488, -0.7502357305872309, -0.39943295077666746, 0.005238142973407675, 0.39018099381053084, 0.6867671003418248, 0.8436890183431321, 0.836596113531429, 0.6731284042785624, 0.3921670100355581, 0.05710572682485087, -0.25594001896204605, -0.47303258362576905, -0.5377093741147562, -0.42366952602824715, -0.14210806887028907, 0.25820757487355717, 0.6987248186239601, 1.08581500400782, 1.3299538680659906, 1.36576608776962, 1.1687968307996734, 0.7651468624418765, 0.23121383399282713, -0.3174206495623736, -0.7467329175059213, -0.9312459628534183, -0.7822123340390011, -0.27115881270767295, 0.5566689652908178, 1.5828606193603665, 2.631744320351552, 3.499896618598963, 3.9944809360137143, 3.973311904565126, 3.378493839219502, 2.2560563123912294, 0.7562396902494246, -0.8873538060115487, -2.3972728706822566, -3.503824241325222, -3.9991523951928554, -3.7829045927175264, -2.8895300519712195, -1.4903691001812343, 0.131539239222761, 1.6304716051637211, 2.662245924159934, 2.9514113473461716, 2.3479117640102563, 0.8612877929376477, -1.3353490500193603, -3.933329554269919, -6.543567178658247, -8.768155932218141, -10.274066004098762, -10.85389648884432, -10.461219115628172, -9.213392949781074, -7.361713948572239, -5.235839454068161, -3.174985417586584, -1.4611352188266655, -0.26875674607992733, 0.35855686893069594, 0.5005838237237381, 0.3255034747042204, 0.037281005581868434, -0.18082385438493967, -0.2123592505660725, -0.032207747268882814, 0.295779518321173, 0.6461970018699706, 0.8761050271369569, 0.8729064048999956, 0.5924603539907966, 0.07663436133761203, -0.5547306412862159, -1.1352813132001882, -1.498240448423254, -1.5240790764108032, -1.1761001668266575, -0.5134965302721904, 0.3222892781444382, 1.1444895410889744, 1.7710360215671408, 2.073513184529904, 2.0108996974620252, 1.6381240034856503, 1.0866804591552912, 0.5228126898052374, 0.09566577694385298, -0.10877005632546131, -0.09333311908442338, 0.0538723533431271, 0.19238455450847322, 0.1824794376622068, -0.05771334970512073, -0.5097115050555692, -1.0423135852070569, -1.4367199891704212, -1.4454038728196261, -0.8701035656242707, 0.36308354020440503, 2.1549251295298038, 4.228529748279602, 6.175717515367974, 7.546705760806973, 7.9623119852814455, 7.219585963610122, 5.361174605297435, 2.68650772312174, -0.3025987203959167, -3.011800150159213, -4.893668011293149, -5.581417501046603, -4.981487236104846, -3.299192111140749, -0.9888176055506472, 1.3603472887019405, 3.1729662148887128, 4.032513306682341, 3.7835073872396894, 2.5638288898102544, 0.7587801848604034, -1.1099925976226377, -2.529675220761792, -3.135251382012899, -2.804042572421102, -1.6805006305116614, -0.12594338144071457, 1.3907298657736493, 2.4288153454905252, 2.698682366354586, 2.137046760196519, 0.9146693026858519, -0.6232035734491647, -2.0636204356554932, -3.046638514907238, -3.3637717090330495, -3.0060781594669503, -2.150190835571264, -1.0900406265458795, -0.1383995438088256, 0.46937319070030226, 0.6392690698968746, 0.4319386283847958, 0.0243418027611556, -0.3642766745318329, -0.5549501905148603, -0.47123250803338756, -0.16035932742375122, 0.23242350414566812, 0.5254325578814691, 0.574502377437793, 0.3316770562264328, -0.1332518294128698, -0.6566208891147167, -1.0417400644812933, -1.1344306246800113, -0.8850445471905757, -0.37303005526936883, 0.21669034221698869, 0.6586652783159083, 0.7705863601565185, 0.48503720915265547, -0.11842700259091991, -0.8353050846025063, -1.407333988253794, -1.6191836053962134, -1.3858566943979165, -0.7968980431864428, -0.09693249262380792, 0.396056556848146, 0.4102452070033318, -0.16319354229235244, -1.1991642269806617, -2.3444258472191906, -3.106520822463088, -3.0037444632219703, -1.7309093917088698, 0.7136739903069625, 3.985985201551179, 7.460091784733371, 10.385708396504823, 12.095802209855872, 12.201739445753967, 10.714247185565245, 8.049450475045308, 4.914336591713832, 2.1041513309459767, 0.2729952007856352, -0.25145871082979643, 0.44870021118902825, 1.926036408026034, 3.5249858229921878, 4.600714206503452, 4.728751831223964, 3.8379562262479108, 2.2248554838606736, 0.44659653507976815, -0.8704520750886294, -1.242165113301015, -0.48828283215063284, 1.2080662900066663, 3.3604406947999736, 5.336312622467481, 6.55741465083116, 6.676459286457502, 5.67353511794584, 3.8443088436652504, 1.6893904716316532, -0.25318970798577406, -1.573579823990467, -2.0991100260907696, -1.9149012456943526, -1.2970327539783106, -0.5897709886211001, -0.07582551864258445], 'positive_zeros': ['0.852842285448942225754693816618488', '3.23095991775238003884677667742252', '4.19966145721122117467101804997959', '5.12339211448574239808331945169430', '6.02132035548371504795507392951576', '6.67257899514189871944796635446406', '7.67637871918699686789550025777453', '8.295774499804542427753772962716439', '9.432631514221575980545528509189817', '10.36488025849131436839282840170150'], 'prelabel': '2-3e6-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -3.0768312803133384e-61, 'root_number': '1.0 - 9.666150546567661e-61*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.000000000000000000000000000000000000000000000000000000000000153841564016', 'prec': 250}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.852842285448942225754693816618', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.23095991775238003884677667742', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.19966145721122117467101804998', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '9.7', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/c/d/487/5'], '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': '2-3e6-9.7-c1-0-6', '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': '2-3e6-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -1.5384156401566692e-61, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.852842285448942225754693816618', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1081106035049366566222365666583', 'Lhash_array': ['1081106035049366566222365666583'], 'label': '2-3e6-9.7-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/c/d/487/5'}