-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2881533737061252523382527755145', 'a10': [-258.35589737329366, 0.0], 'a2': [10.334235894931746, 0.0], 'a3': [-10.778647439142647, 0.0], 'a4': [74.79643153209575, 0.0], 'a5': [-25.0, 0.0], 'a6': [-111.38908526440208, 0.0], 'a7': [0.0, 0.0], 'a8': [442.26841891397277, 0.0], 'a9': [-126.82075938266367, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 39.294035854180265, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [25.0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 7], 'central_character': '245.1', 'coefficient_field': 'CDF', 'conductor': 245, 'conductor_radical': 35, 'degree': 2, 'euler_factors': [[[1.0, 0], [-10.334235894931746, 0], [32.0, 0]], [[1.0, 0], [10.778647439142647, 0], [243.0, 0]], [[1.0, 0], [25.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [262.9171596274878, 0], [161051.0, 0]], [[1.0, 0], [688.9266460829846, 0], [371293.0, 0]], [[1.0, 0], [1678.0776692374063, 0], [1419857.0, 0]], [[1.0, 0], [925.1086615167578, 0], [2476099.0, 0]], [[1.0, 0], [-4608.330004873891, 0], [6436343.0, 0]], [[1.0, 0], [3413.297912285531, 0], [20511149.0, 0]], [[1.0, 0], [-5534.3428379988345, 0], [28629151.0, 0]], [[1.0, 0], [14971.763986359763, 0], [69343957.0, 0]], [[1.0, 0], [14959.668442452316, 0], [115856201.0, 0]], [[1.0, 0], [19652.746449715152, 0], [147008443.0, 0]], [[1.0, 0], [-11298.986302311481, 0], [229345007.0, 0]], [[1.0, 0], [21380.68099806665, 0], [418195493.0, 0]], [[1.0, 0], [-3476.3111473607287, 0], [714924299.0, 0]], [[1.0, 0], [-22396.10072145696, 0], [844596301.0, 0]], [[1.0, 0], [-44935.786848768905, 0], [1350125107.0, 0]], [[1.0, 0], [-10904.879581362713, 0], [1804229351.0, 0]], [[1.0, 0], [-9209.406123322706, 0], [2073071593.0, 0]], [[1.0, 0], [3355.91906029169, 0], [3077056399.0, 0]], [[1.0, 0], [45537.734910933315, 0], [3939040643.0, 0]], [[1.0, 0], [-52889.08424504653, 0], [5584059449.0, 0]], [[1.0, 0], [-164527.1886698014, 0], [8587340257.0, 0]], [[1.0, 0], [24002.96945512963, 0], [10510100501.0, 0]], [[1.0, 0], [-110338.5457125203, 0], [11592740743.0, 0]], [[1.0, 0], [-90804.26485168721, 0], [14025517307.0, 0]], [[1.0, 0], [-141519.57536184738, 0], [15386239549.0, 0]], [[1.0, 0], [116848.006475101, 0], [18424351793.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 64, 'label': '2-245-1.1-c5-0-64', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/245/6/a/l/1/10', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [-3.9708185376508496e-60, 0.49120334496503043, 0.9771094007462832, 1.4524729622096824, 1.9121531312273243, 2.3511657842279674, 2.7647363249735104, 3.148352669026674, 3.4978182870770373, 3.809304994976427, 4.079405025090112, 4.305181753278698, 4.484218295952378, 4.614663040008663, 4.69527103302325, 4.7254400496349165, 4.7052400701019685, 4.635434865343525, 4.517494385383888, 4.353596699862146, 4.14661834369574, 3.900112080105715, 3.618271307312759, 3.3058806027121137, 2.968252215654986, 2.611148681464566, 2.240692127278891, 1.863261264994494, 1.4853775063300634, 1.1135820764742748, 0.7543064311328297, 0.413738681185319, 0.09768908311718373, -0.18854205468698432, -0.44029048593333436, -0.6536444762302186, -0.8255478900572485, -0.953886319225853, -1.0375528850576534, -1.0764907032721542, -1.0717094859354388, -1.0252743638075787, -0.9402657350768263, -0.8207097676912014, -0.6714800821186108, -0.49817209438387533, -0.30695247629107325, -0.10438715783461107, 0.10274777980997565, 0.3076671309954615, 0.5037836006738234, 0.6849143710783252, 0.8454803478473787, 0.9806910774627144, 1.086708414941477, 1.1607823669699906, 1.2013531484983755, 1.208114367765142, 1.182033382647498, 1.1253262258771908, 1.0413860426322452, 0.934665675244316, 0.8105168104570107, 0.6749899107712375, 0.5346009125359695, 0.3960723152805652, 0.26605773389928195, 0.1508601642147503, 0.05615505494666083, -0.01327027440347828, -0.05374932745979027, -0.0629301680207132, -0.03992009673223036, 0.014627384209516035, 0.09849005714037463, 0.20792333874388674, 0.33777723692825296, 0.4816827343142454, 0.6323033475149832, 0.7816445166555142, 0.921410493121325, 1.0433956533138269, 1.1398948097938746, 1.204115249570517, 1.230572020384085, 1.2154475082289415, 1.156896676331611, 1.0552805100148688, 0.9133122411154805, 0.73610377974739, 0.531103390662822, 0.30791990750780646, 0.0780335349948415, -0.14560163267665774, -0.3490530554259576, -0.5179877490682453, -0.6383127077275134, -0.6968534618941539, -0.6820431532758405, -0.5845921929472503, -0.39810744662646025, -0.11963008969080158, 0.2499371280220483, 0.7055394538381599, 1.2378384031857728, 1.8332549530962698, 2.474197164419676, 3.1394741846882424, 3.804890486641469, 4.444005895821043, 5.029038822670528, 5.53188252320471, 5.9251975478050065, 6.18353815923684, 6.284466728193828, 6.209608209888285, 5.9455969574678456, 5.484870439696747, 4.8262689071307925, 3.9754065962947935, 2.9447884750912734, 1.7536565154119819, 0.42756064111427716, -1.0023386243437913, -2.5002167188640936, -4.0267500177688, -5.540457661159298, -6.999169376884836, -8.361561130166802, -9.588695522632422, -10.645501687966034, -11.50213019683119, -12.135122262980547, -12.528339263235829, -12.673608026088177, -12.57104914371416, -12.22906922615075, -11.664012939131764, -10.899486158947948, -9.965376896314897, -8.896615027797221, -7.731724591107259, -6.511232773945655, -5.276007177873428, -4.06559702411289, -2.9166544024908054, -1.8615083440077203, -0.9269575100974483, -0.13333691983556384, 0.506099152395066, 0.9854515486197133, 1.3060983938811745, 1.4762733126294905, 1.5103253982106015, 1.4277028755562973, 1.251716536491016, 1.0081502781386764, 0.7237937885016376, 0.42497613174181, 0.1361784340009849, -0.12120096368691088, -0.3298644182909013, -0.4773640099747402, -0.5565451890930019, -0.5656661214704476, -0.5081924975616406, -0.3922863179543251, -0.23002488549642422, -0.036401877184592465, 0.1718250054414215, 0.377366480597237, 0.5636364358557476, 0.7159114130166895, 0.8223421995193033, 0.8747543155467657, 0.8691875577817099, 0.8061413120558861, 0.6905110931940003, 0.5312215720312187, 0.3405809802557669, 0.13340000363898735, -0.07406609217957034, -0.26528134767014755, -0.4246206891270333, -0.5385083315268514, -0.5964248427604207, -0.5917125961944433, -0.5221219890982675, -0.39005748032268067, -0.20250218576904125, 0.029378772316758246, 0.29093411972463845, 0.5649786537730775, 0.8329406740235548, 1.0761288791832202, 1.2770332263121567, 1.4205700775353767, 1.49518380337512, 1.493724901860878, 1.414038254330449, 1.2592136046554392, 1.0374725967882825, 0.7616913244524067, 0.44858272089984164, 0.11758752890237076, -0.21045566402781857, -0.5147733407168537, -0.7761530198724172, -0.9783670412521965, -1.1094207748278906, -1.1625309689041634, -1.1367559505389213, -1.037221402430381, -0.8749121431596576, -0.6660300412679723, -0.4309489393618685, -0.19282715082193552, 0.024035385959071162, 0.19598681557420933, 0.30183686800332116, 0.3245645794857801, 0.25279298708338926, 0.08191489846782567, -0.185226242202134, -0.5381689322085949, -0.9592148272326881, -1.4243566280580904, -1.9047121138198033, -2.368386475629352, -2.782651648697495, -3.116304223226162, -3.3420448621591334, -3.4387135923295866, -3.393217855482998, -3.202004071567487, -2.8719481712507067, -2.4205748250584715, -1.875556954163193, -1.2734939787569204, -0.6580161308244571, -0.0773097682187495, 0.41879831611448903, 0.7820241903485255, 0.9688792158146491, 0.943780481162455, 0.6818091410586867, 0.1709217006838465, -0.5865520173347687, -1.5732497230268403, -2.7570313508263737, -4.092165523818438, -5.52140564526039, -6.978854361044895, -8.393460986367879, -9.69295107089305, -10.80795386918602, -11.676074637318166], 'positive_zeros': ['2.27312931224302467961178707323906', '3.34017073998184507281108673100728', '4.83567140378609100515879814365449', '5.11733264437658635675443882788607', '6.49284686452283808900517150744879', '7.12626539862198594140891431569409', '8.599613728069086516030396174758910', '10.41957847493319476436960878431604', '11.21549095824338804720739150306422'], 'prelabel': '2-245-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.268495501647925, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.27312931224302467961178707324', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.34017073998184507281108673101', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.83567140378609100515879814365', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 39.294035854180265, 'bad_primes': [5, 7], 'central_character': '1.1', 'conductor': 245, 'conductor_radical': 35, 'degree': 2, 'index': 64, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/245/6/a/l/1/10'], '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': '2-245-1.1-c5-0-64', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-245-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.268495501647925, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '2.27312931224302467961178707324', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2881533737061252523382527755145', 'Lhash_array': ['2881533737061252523382527755145'], 'label': '2-245-1.1-c5-0-64', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/245/6/a/l/1/10'}