-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1647193105392582456540113597661', 'a10': [0, 0], 'a2': [2.2251425457512526, 1.284686647774775], 'a3': [0, 0], 'a4': [2.300839565941577, 3.9851710282755337], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-0.15175469703438862, -2.64139556142733], 'a8': [0, 6.684684885049112], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.576438318351666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.15175469703438862, 2.64139556142733]]]], 'bad_primes': [3, 5, 7], 'central_character': '1575.26', 'coefficient_field': 'CDF', 'conductor': 1575, 'conductor_radical': 105, 'conjugate': '1966672208588985492150258747664', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.2251425457512526, -1.284686647774775], [1.0, 1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.15175469703438862, 2.64139556142733]], [[1.0, 0], [-4.881889744096956, 2.8185603579084506], [5.5, -9.526279441628825]], [[1.0, 0], [0, -3.535369072645827], [-13.0, 0]], [[1.0, 0], [-2.6714164908325477, -4.627029090299331], [-8.5, 14.722431864335457]], [[1.0, 0], [-1.2494172399103067, -0.7213513797923748], [9.5, 16.454482671904334]], [[1.0, 0], [2.5968641195561566, 1.4993001984746275], [11.5, 19.91858428704209]], [[1.0, 0], [0, -2.1940424944418364], [-29.0, 0]], [[1.0, 0], [-1.318991111128167, 0.7615198730685707], [15.5, -26.846787517317598]], [[1.0, 0], [0.5465717254740079, -0.9466899985015702], [-18.5, -32.04293994002423]], [[1.0, 0], [6.520579486442208, 0], [41.0, 0]], [[1.0, 0], [-0.48612466281046135, 0], [43.0, 0]], [[1.0, 0], [2.1281618714601565, -3.686084488099857], [-23.5, -40.703193977868615]], [[1.0, 0], [-3.4831848300635238, 2.011017699274396], [26.5, -45.89934640057525]], [[1.0, 0], [5.709779486004282, 9.889628169773927], [-29.5, 51.09549882328188]], [[1.0, 0], [-6.069573871217861, -3.5042701084139507], [30.5, 52.827549630850754]], [[1.0, 0], [1.2448981479824046, 2.1562268425539233], [-33.5, 58.023702053557386]], [[1.0, 0], [0, 8.138488758573175], [-71.0, 0]], [[1.0, 0], [2.7176052146781022, -1.5690101022455332], [36.5, -63.21985447626402]], [[1.0, 0], [-6.402518697824731, 11.089487681042163], [-39.5, -68.41600689897065]], [[1.0, 0], [6.772408311544854, 0], [83.0, 0]], [[1.0, 0], [5.165131217638641, -8.946269696710226], [-44.5, -77.07626093681505]], [[1.0, 0], [0, -14.732077984022862], [-97.0, 0]], [[1.0, 0], [7.4668278215404404, 12.93292515827688], [-50.5, 87.4685657822283]], [[1.0, 0], [3.3905802299601975, 1.9575524084765432], [51.5, 89.20061658979718]], [[1.0, 0], [12.836256137805053, 7.411015936548734], [53.5, 92.66471820493493]], [[1.0, 0], [-5.519317065365977, -9.559737580295826], [-54.5, 94.39676901250381]], [[1.0, 0], [0, 7.543139087848522], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 32, 'label': '2-1575-21.5-c1-0-32', 'leading_term': '4.599822106659497443208266837142976406799363168215724844', '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/1575/2/bk/i/26/11', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [4.599822106659498, 4.486563276234329, 4.367997317213232, 4.2435073656404825, 4.112149167561427, 3.972753970415017, 3.8240400538741617, 3.6647260593386988, 3.4936400177092475, 3.309819157585087, 3.112596913683373, 2.9016748119478515, 2.6771779382797805, 2.4396934504305228, 2.1902920873844405, 1.930532928651815, 1.6624518318745845, 1.3885340999971298, 1.1116720523097867, 0.8351083316077812, 0.562365989753046, 0.29716665904889594, 0.043338429378612174, -0.19528460396247982, -0.4149687990056783, -0.6121907612079779, -0.7837474856806457, -0.9268635995955944, -1.0392922729454708, -1.1194062781705043, -1.1662757040726563, -1.179728979521443, -1.1603941458743516, -1.1097177368888045, -1.029959178738529, -0.9241593022090364, -0.7960823498131618, -0.6501317420052475, -0.4912408127353115, -0.32474070397317184, -0.15620858592441234, 0.00869969439663472, 0.16442757951827885, 0.3057006949819438, 0.42770841369792645, 0.5262774656589598, 0.5980308287204508, 0.6405252524129206, 0.6523611539208363, 0.6332592892622576, 0.5840995379184591, 0.5069183282665434, 0.40486264442242614, 0.28210015067570415, 0.143686694456592, -0.004605760349466764, -0.15649593198428371, -0.30542820908726653, -0.4448277425617681, -0.5683662499154932, -0.6702281486537358, -0.7453660215014394, -0.7897342349200666, -0.800489822369034, -0.7761505256329032, -0.7167011612635666, -0.6236412224593728, -0.4999687941794318, -0.3500983828757665, -0.17971305244148195, 0.004445793539290986, 0.19484466003347922, 0.3834710326295509, 0.5621814224238386, 0.7230702658677415, 0.8588438030931617, 0.9631819240387179, 1.0310705570275398, 1.0590875471244359, 1.0456261668944213, 0.991042418687783, 0.8977150845554356, 0.7700109763641774, 0.6141519143646186, 0.4379844607897542, 0.25065816813751957, 0.06222285731670311, -0.11684000926267127, -0.2761326840910943, -0.40588060225999767, -0.49747077892980773, -0.5439624538038953, -0.5405430038624613, -0.48490314847451715, -0.37750780869400985, -0.2217426276328206, -0.0239210174670448, 0.20685748920949534, 0.4590000631776087, 0.7188597623307252, 0.971308737974975, 1.2004257335061486, 1.3902712554304033, 1.525717782399373, 1.5932975919981562, 1.5820275414259226, 1.4841686937333807, 1.295879218919022, 1.017721614197359, 0.6549899773295558, 0.21782972419801122, -0.2788694451023725, -0.8158166711555598, -1.3698975948844094, -1.9149735401609123, -2.4228777277122435, -2.8645730923555037, -3.211426455592367, -3.436545650801481, -3.516120204307523, -3.430702756515437, -3.1663678698099065, -2.7156873918767706, -2.078467157364969, -1.2621983958198684, -0.2821884917166419, 0.8386507148060423, 2.070363654085553, 3.376851080067055, 4.717083221194119, 6.046583819386682, 7.319128236232041, 8.488586351343665, 9.510831393606807, 10.345629729289211, 10.958424427704875, 11.321927399712044, 11.417441118062177, 11.235841227752658, 10.778165369434033, 10.055770694632159, 9.090042089821141, 7.911654138444511, 6.559411318708802, 5.078711784634869, 3.519699228972407, 1.9351837531488485, 0.3784254553807367, -1.09911716002721, -2.449968396450804, -3.632642433272184, -4.613379539955347, -5.367526813460973, -5.880495410538915, -6.148246575587407, -6.177281838366483, -5.984137412751348, -5.594407795332682, -5.041347523966761, -4.364121721248206, -3.6057942251325454, -2.811155774718866, -2.024503077845874, -1.287482120736931, -0.6371055833503136, -0.10404482319929234, 0.28871795835473674, 0.5268112822765022, 0.6049267733775324, 0.5267849867454427, 0.30462382314181424, -0.04175532319806166, -0.48632452705602325, -0.9984695915281971, -1.5448376846088034, -2.0912858177613787, -2.604819134437795, -3.0554098746977014, -3.4175960770098976, -3.67177309860685, -3.805110060318955, -3.8120462248998317, -3.6943477334924006, -3.4607315270414665, -3.1260890733693087, -2.7103661398665784, -2.2371748550726602, -1.7322294643789853, -1.22170657455484, -0.7306337232233912, -0.28140662263837474, 0.1074743572961886, 0.4223733530603819, 0.6551388281798985, 0.8033425567196374, 0.8701316238106608, 0.8637128476825233, 0.7965131099280922, 0.6840801123355645, 0.5438046693526469, 0.3935566909364656, 0.25033176927689654, 0.12900342832255288, 0.041267742893001676, -0.005147260501277332, -0.006954283972601643, 0.0345686713668992, 0.1138069903076968, 0.2213711136170121, 0.3449469099041799, 0.47036954734806385, 0.5828393346921756, 0.6681874533416806, 0.7140955356698475, 0.7111760050493836, 0.6538298418560295, 0.5408143544393327, 0.3754745444983054, 0.16561631177786815, -0.0769736916113306, -0.33733017323610814, -0.5983772483661275, -0.8421855065829921, -1.051325646741536, -1.2102172893703, -1.3063700111406609, -1.33141972112141, -1.281876924616209, -1.1595233648275904, -0.9714186659102891, -0.7295071811327737, -0.44984523868625753, -0.1514981818706177, 0.14481717231164729, 0.4182478124699137, 0.6493662103422894, 0.821660550827332, 0.9228378637839577, 0.9458353895055815, 0.8894547178139961, 0.7585594843976594, 0.5638089384712448, 0.3209343164896736, 0.04960017103182777, -0.22807400975157252, -0.48922795627768906, -0.7120848974025573, -0.8777473634947033, -0.9718229952284574, -0.9857465463739064, -0.9176824076604323, -0.772919581148725, -0.5637063930024069, -0.3085130012263554, -0.030753099468285517, 0.24296099340705724, 0.48491664505142473], 'positive_zeros': ['1.29940624419380209903792351781191', '2.39918687159361890805456172675567', '3.22087037726722647842282521428537', '4.10018063818980716899429884452816', '5.05890758852029898452790272382807', '5.63143428225782467408084209567507', '6.47175376355331732135847610520226', '7.33962637614355359250552580821508', '8.627917008016240737591742433821168', '9.681529349468383756965490021863178'], 'prelabel': '2-1575-21.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.546327440938254, 'root_angle': -0.44867509196839644, 'root_number': '0.16054417432041974730488180705500032902623674961250023031 - 0.9870286561654502828037727395498649583618057581626333507*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.22433754598419822', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.29940624419380209903792351781', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.39918687159361890805456172676', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.22087037726722647842282521429', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 12.576438318351666, 'bad_primes': [3, 5, 7], 'central_character': '21.5', 'conductor': 1575, 'conductor_radical': 105, 'degree': 2, 'index': 32, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1575/2/bk/i/26/11'], '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': '2-1575-21.5-c1-0-32', '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': '2-1575-21.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.546327440938254, 'root_angle': -0.22433754598419822, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.29940624419380209903792351781', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1647193105392582456540113597661', 'Lhash_array': ['1647193105392582456540113597661'], 'label': '2-1575-21.5-c1-0-32', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1575/2/bk/i/26/11'}