-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '4681212610231288363785672148605', 'a10': [-1.3020800468270108, -2.2552687966260456], 'a2': [0.7132203932344198, -0.41177798602542304], 'a3': [-1.3301460025945884, -2.303880457978471], 'a4': [-0.660877780449693, 1.144673893332218], 'a5': [0.0, -3.162092416340637], 'a6': [-1.897374510059408, -1.0954496841363335], 'a7': [0.8660254037844386, 0.5], 'a8': [0.0, 2.735651629871797], 'a9': [-2.038576776436726, 3.5309185519183894], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-0.8660254037844386, -0.5]]], [13, [[1.0, 0], [0.07661926980187603, -3.6047370899269517]]]], 'bad_primes': [7, 13], 'central_character': '91.36', 'coefficient_field': 'CDF', 'conductor': 91, 'conductor_radical': 91, 'conjugate': '1874325318352566507354861107064', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7132203932344198, 0.41177798602542304], [1.0, -1.7320508075688772]], [[1.0, 0], [1.3301460025945884, 2.303880457978471], [-1.5, 2.598076211353316]], [[1.0, 0], [0, 3.162092416340637], [-5.0, 0]], [[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [-5.146526168841176, 2.9713482689719064], [5.5, -9.526279441628825]], [[1.0, 0], [0.07661926980187603, -3.6047370899269517]], [[1.0, 0], [1.3498215166669636, -2.337959448016861], [-8.5, -14.722431864335457]], [[1.0, 0], [-1.694853413941645, -0.9785240747761649], [9.5, 16.454482671904334]], [[1.0, 0], [1.3647074113470563, 2.363742573918901], [-11.5, 19.91858428704209]], [[1.0, 0], [-2.9992257482919755, -5.194811379410487], [-14.5, 25.11473670974872]], [[1.0, 0], [0, 1.1515483401279167], [-31.0, 0]], [[1.0, 0], [5.633096987961099, -3.2522700623706102], [18.5, -32.04293994002423]], [[1.0, 0], [3.233514563252414, -1.8668705035223563], [20.5, -35.50704155516198]], [[1.0, 0], [-3.4956249259890555, 6.054599976017241], [-21.5, -37.239092362730865]], [[1.0, 0], [0, -0.45607087976923866], [-47.0, 0]], [[1.0, 0], [-0.3992860666678545, 0], [53.0, 0]], [[1.0, 0], [-4.1619985174519805, -2.4029309644177244], [29.5, 51.09549882328188]], [[1.0, 0], [-0.5785135798419923, 1.002014913154885], [-30.5, -52.827549630850754]], [[1.0, 0], [5.437929969410293, -3.139590331673366], [33.5, -58.023702053557386]], [[1.0, 0], [-3.9033455097990624, -2.2535975808226056], [35.5, 61.48780366869514]], [[1.0, 0], [0, -8.305751717159824], [-73.0, 0]], [[1.0, 0], [7.914096299104659, 0], [79.0, 0]], [[1.0, 0], [0, -6.197946350897463], [-83.0, 0]], [[1.0, 0], [-3.0842307479878355, 1.7806814525936976], [44.5, -77.07626093681505]], [[1.0, 0], [2.9683101710707396, 1.7137546763059954], [48.5, 84.00446416709055]], [[1.0, 0], [6.664744969113536, 11.543676905993712], [-50.5, 87.4685657822283]], [[1.0, 0], [11.64495664083694, 0], [103.0, 0]], [[1.0, 0], [1.964829086458057, 3.403183805934497], [-53.5, 92.66471820493493]], [[1.0, 0], [0, -11.253324356642585], [-109.0, 0]], [[1.0, 0], [-2.8870897583240893, 5.000586147429074], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-91-13.10-c1-0-4', '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/91/2/q/a/36/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.9802295204763956, 1.0526193596052753, 1.141686480671583, 1.2490842013503065, 1.3753223958223695, 1.5198558571799532, 1.6811931498224555, 1.856977222079788, 2.0440254607322728, 2.238342753679819, 2.435131498752522, 2.6288224613119815, 2.8131458535632543, 2.981256368563168, 3.1259203354532112, 3.2397677647793612, 3.315606609919487, 3.346790923142254, 3.3276287472521697, 3.253809757302392, 3.1228272128326244, 2.9343641810550465, 2.6906107999868842, 2.39647814162286, 2.05967554149468, 1.6906225078177732, 1.3021737612062512, 0.9091465952714191, 0.5276533057547876, 0.17425729676282098, -0.13501131927795226, -0.385727533365174, -0.5661617603082263, -0.6683071293048072, -0.6887544762432547, -0.6293245391314605, -0.4973733980959739, -0.30570226750213053, -0.07202640698412056, 0.18201058765327316, 0.43225318308745536, 0.6538157772316006, 0.8231232628034982, 0.9200656322274989, 0.9300920023077037, 0.8460515094849141, 0.6695862192875143, 0.4118970693512527, 0.09373903220489554, -0.25544455707195535, -0.5992689319363809, -0.896975771330739, -1.1066764873098462, -1.1890437199819954, -1.1111545246525745, -0.8501404999956532, -0.3962806165635674, 0.24481260769937216, 1.0512109919443342, 1.9851020088491034, 2.994723790812033, 4.017752916840209, 4.985943404125931, 5.830670273557576, 6.488907891626357, 6.90908773391119, 7.056245557934169, 6.915893244511734, 6.496138979231698, 5.827727342762667, 4.961867379002805, 3.965944182232801, 2.9174449584427435, 1.896647612113755, 0.9787920137442936, 0.22655731217670222, -0.31631496569624934, -0.6294919002382388, -0.7180281153615126, -0.611521650314599, -0.3604276277537839, -0.029845728688932604, 0.30858332430944757, 0.585774375855533, 0.7442202114790138, 0.7458241793864022, 0.5775153547525955, 0.25384085164541, -0.18393226763115475, -0.6722550662528004, -1.1328748164456997, -1.4827282811170603, -1.6449824193874243, -1.5598440686050288, -1.1937180982625484, -0.545436311888882, 0.3514006334897474, 1.4304610217712983, 2.5990364667896264, 3.7480732488187107, 4.764721293654299, 5.545853259420268, 6.010810239366576, 6.1116644747309135, 5.839560577174083, 5.226179220379081, 4.340003539079201, 3.2777756816652373, 2.152211347565211, 1.0775945025381704, 0.15521670077913274, -0.5393038862488782, -0.9650118398494206, -1.1195970969019746, -1.0377634368369137, -0.7841969522460469, -0.44216408674069396, -0.09945374069894906, 0.16617833193108644, 0.29978074631446117, 0.27813983481447624, 0.11338153793343372, -0.14943505632905252, -0.4404549982638159, -0.6776728930549936, -0.7820806973236569, -0.6928255691476742, -0.37978839388261243, 0.1486796814244981, 0.8444083731791765, 1.6249849150025764, 2.3856483159280595, 3.0157933339980985, 3.417508177008201, 3.5230910585588613, 3.3085017818383564, 2.8002294617705097, 2.074035170173795, 1.2453179198962796, 0.45225290709253396, -0.16586840081868046, -0.49172872434310877, -0.45071958703029946, -0.02573188313082576, 0.7367727184969937, 1.7308635349022379, 2.805239545515836, 3.7854709261537995, 4.501086499353811, 4.8132580076034195, 4.638554364127805, 3.9647119963082127, 2.855541752885314, 1.4437964436123376, -0.08721462245833708, -1.5305827785686652, -2.6871467946924823, -3.396211373000785, -3.5606126404875953, -3.161953579407185, -2.263410833989125, -0.9995679856245547, 0.4450876760366678, 1.8654367315766482, 3.067863414908177, 3.899857078274403, 4.272129193338077, 4.169620166092686, 3.649743738294936, 2.8284894951808264, 1.8571647452263647, 0.8942078860728592, 0.07733637957525903, -0.49885804774597536, -0.7958657225098623, -0.8326344074150317, -0.6755059049364965, -0.41910062626495603, -0.16231365296659914, 0.015459851931397638, 0.0728201751378523, 0.015622447846624688, -0.10504185146412666, -0.2058162496731595, -0.1923317162177269, 0.015777887633756236, 0.46156841665873566, 1.1344936414296147, 1.9651538203935772, 2.832933482833312, 3.5857250397175253, 4.068336102643461, 4.1541718095571865, 3.773806838798272, 2.9343586482221284, 1.725135645225993, 0.30759356017922, -1.1092925756573297, -2.304151805091588, -3.0824692619541447, -3.312516998001945, -2.950889580505177, -2.052380593962882, -0.7618618520978289, 0.7106897595159821, 2.127522896473554, 3.2657731259372262, 3.9572526576214995, 4.1176210193696505, 3.759221018439645, 2.9850916099505134, 1.9654531335130312, 0.9015300141308987, -0.015813492229440878, -0.6440595902406488, -0.9157678344360136, -0.8485245070320286, -0.536132003402907, -0.12307145073551637, 0.23210023614928083, 0.3962985780027407, 0.2955470565438484, -0.0649795484881044, -0.5993033132469543, -1.1581886248543858, -1.5624288943036975, -1.6448132573971623, -1.2915693365948178, -0.47390595449131934, 0.7378313216464168, 2.1812867132855653, 3.629843012341835, 4.835787226815151, 5.580147254475408, 5.718720536420167, 5.214316587475703, 4.147918365505766, 2.7058007700881945, 1.1447215871161738, -0.2579696502095162, -1.259114453049725, -1.6980252592852831, -1.52810438835817, -0.8250896474603315, 0.22985319821530337, 1.3886122237048069, 2.3879916162867203, 3.0039088325922423, 3.0964313950015447, 2.636220758468711, 1.7070756421220825, 0.4845391547875058, -0.8042254817028485, -1.9300532723509376, -2.7097341471058027, -3.041774291569765, -2.922435012506929], 'positive_zeros': ['3.69282561723906964847530201773182', '4.78596105179415781043020818010830', '6.03414898312384266644644028519905', '7.08122048986503234780724096657562', '9.421178181167146303666712323804073', '10.13575811931214917327827468830125', '10.95034129633082295264378016601685', '11.95453800125988746864020045300799', '13.77438978196193640930151428532129', '14.66625402390913518144048519476146'], 'prelabel': '2-91-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': 0.5108466122910795, 'root_number': '-0.034069043390374906 + 0.9994194816404495*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.255423306146', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.69282561723906964847530201773', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.78596105179415781043020818011', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.03414898312384266644644028520', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'bad_primes': [7, 13], 'central_character': '13.10', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/91/2/q/a/36/4'], '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': '2-91-13.10-c1-0-4', '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': '2-91-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': 0.25542330614553976, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.69282561723906964847530201773', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '4681212610231288363785672148605', 'Lhash_array': ['4681212610231288363785672148605'], 'label': '2-91-13.10-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/2/q/a/36/4'}