-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1981821050851521278223292517828', 'a10': [-0.13654561404870313, -0.4380696406894943], 'a2': [-0.5205582696804028, -1.3149217040825454], 'a3': [1.3231413628291, 0.9021025065693768], 'a4': [-1.4580381757346903, 1.3689867340848327], 'a5': [0.32355361351194956, 0.024246991323460296], 'a6': [0.4974219868184544, -2.209424215447451], 'a7': [1.281652910282987, 2.3145984138859057], 'a8': [2.559104199137648, 1.2045686771438386], 'a9': [-0.1591089394286894, -0.4054029660251078], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5650678796170963, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5205582696804028, 1.3149217040825454]]], [7, [[1.0, 0], [-1.281652910282987, -2.3145984138859057]]]], 'bad_primes': [2, 7], 'central_character': '196.103', 'coefficient_field': 'CDF', 'conductor': 196, 'conductor_radical': 14, 'conjugate': '2499888492378782060741388075507', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5205582696804028, 1.3149217040825454]], [[1.0, 0], [-1.3231413628291, -0.9021025065693768], [1.0960230730991851, 2.792621245932613]], [[1.0, 0], [-0.32355361351194956, -0.024246991323460296], [4.944154131125643, 0.7452113308808722]], [[1.0, 0], [-1.281652910282987, -2.3145984138859057]], [[1.0, 0], [-2.6113065381702114, -1.024862294139537], [8.063570590128089, 7.481900115480113]], [[1.0, 0], [-2.0121130036351422, 1.6046065758232695], [2.8927721414320873, -12.674062858363706]], [[1.0, 0], [0.2950260265005742, 0.31796243653270456], [-1.2704115909692124, 16.952464552080063]], [[1.0, 0], [3.1932069555008855, -5.5307966860098645], [-9.5, -16.454482671904334]], [[1.0, 0], [-3.320971786483009, 3.5791563660043773], [-1.7187921524877579, -22.93568733516714]], [[1.0, 0], [0.9878211151630376, 4.327927086644752], [-26.128097169170154, 12.582628434409186]], [[1.0, 0], [1.2810188580269648, 2.218789747556565], [-15.5, 26.846787517317598]], [[1.0, 0], [8.400435950680661, 2.591191323965595], [30.57083464969181, 20.842842148354016]], [[1.0, 0], [-3.279836445528509, -6.810650556397708], [-25.563081876208074, 32.05509078118922]], [[1.0, 0], [2.1728807513761237, -4.512033372432696], [-26.81006147992554, -33.61875374612528]], [[1.0, 0], [5.454438404700147, -0.8221243098359718], [44.911921871948614, -13.853493197312499]], [[1.0, 0], [-5.417678677412212, 1.671132553996373], [43.79065503874773, -29.855963077371968]], [[1.0, 0], [-0.18230412419608813, -2.4326794757708425], [-58.34101874728258, 8.793493704394292]], [[1.0, 0], [-2.0244513473202157, 6.563110072630995], [-50.400565233275685, -34.36252354188095]], [[1.0, 0], [-0.8826643790870987, 0.5096065168700303], [33.5, -58.023702053557386]], [[1.0, 0], [11.949665055036768, 2.727433069960154], [63.96878962107176, 30.805745477346626]], [[1.0, 0], [-1.0355575911768917, 6.870475703024722], [-69.75681482238828, -21.51712773199601]], [[1.0, 0], [9.004567599036712, 5.198789527240028], [39.5, 68.41600689897065]], [[1.0, 0], [-3.976575816849095, 4.9864683540374335], [-18.469237518374097, -80.91901671109136]], [[1.0, 0], [-12.67250867500158, 4.973593150908252], [65.24161659285454, -60.53537366161183]], [[1.0, 0], [0, -8.05556883154166], [-97.0, 0]], [[1.0, 0], [-8.365784943871825, 12.270352882473068], [-36.899443461005895, -94.01824861306463]], [[1.0, 0], [0.6411797843766572, -8.55594961776371], [-101.84957510118824, -15.351353416145969]], [[1.0, 0], [2.951573217907001, -1.1584071250189665], [78.43655028579141, -72.77848294148838]], [[1.0, 0], [-6.027898246388911, 15.358834247517931], [-79.90265402945107, -74.13882841703021]], [[1.0, 0], [11.00217231709248, -13.796287713764539], [-25.144865537063527, -110.16685407654607]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-14e2-196.103-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/196/2/p/a/103/11', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.2598650704811962, 1.2553237950170286, 1.2555004354970458, 1.2563900308510578, 1.2522205467454701, 1.2359700147826733, 1.1999021208383207, 1.136071646273063, 1.036806097906158, 0.8951916394769568, 0.7055856193678863, 0.46415930175429415, 0.1694535979918093, -0.17708735538144205, -0.57065335980918, -1.0027330358164557, -1.460966315635749, -1.9292413384328742, -2.3880828865806176, -2.815363027411453, -3.1873415562200624, -3.480015085123121, -3.6707208977239745, -3.7399075144747482, -3.6729515338879635, -3.461873490425275, -3.1067881528550183, -2.616920599832023, -2.0110315585568435, -1.317125660902415, -0.5713645554014048, 0.18382873173384312, 0.9024113263716447, 1.5379628918709878, 2.0473040514815346, 2.3941978856136266, 2.552794520698909, 2.510461524333574, 2.2696617357297852, 1.8485985221035994, 1.2804452701429951, 0.6111054093939436, -0.10439921455422295, -0.8066551529002367, -1.4372950621875051, -1.9446241551650187, -2.2888433840936138, -2.446269928402257, -2.412018980206168, -2.200745484422979, -1.8452416222639836, -1.392927391981481, -0.9005315197831665, -0.4275063983777166, -0.028920073292270195, 0.25131085235492623, 0.3859654174025411, 0.368055193846218, 0.21178104440679668, -0.04935524260186541, -0.367178651543698, -0.6857143555760586, -0.9494616741612116, -1.1119619044467843, -1.1434283796146425, -1.0362499965130523, -0.8074000982429079, -0.4971655083345757, -0.16411433475435686, 0.12321792626281482, 0.29690547426571096, 0.30102067386235615, 0.10213062355640597, -0.3028152661494723, -0.8826751066246744, -1.5733524691516707, -2.2843598207314972, -2.9101852523124245, -3.345148978030769, -3.4997773246852817, -3.316310882787166, -2.7808869159820215, -1.9302357597704354, -0.851392508425845, 0.3261244319712032, 1.4451031116133877, 2.340717766214261, 2.8632826399820046, 2.900465053680544, 2.395603272500361, 1.3591504501322136, -0.12886650682372477, -1.9262301874467218, -3.845150366097599, -5.676055858283961, -7.215295384811805, -8.292735070658825, -8.79509779542769, -8.681407221524585, -7.988024858575965, -6.8223446745217755, -5.345994557508818, -3.750097414093838, -2.226476443321571, -0.9394088986549181, -0.002495215660213844, 0.5356038107078002, 0.6942840313484911, 0.5525893294904409, 0.23089611019931242, -0.1339442961178006, -0.4154674610008931, -0.5215520407522573, -0.4110785841330046, -0.10023519553295557, 0.342659220430444, 0.8127724121752481, 1.191763935715674, 1.3736611809723425, 1.2884691419589374, 0.9187434727606235, 0.3056665560555566, -0.45680959193858695, -1.2388300670734265, -1.8993530576472613, -2.313891108557979, -2.3997158725905634, -2.1333314684258537, -1.5564555334432046, -0.768992015589006, 0.08989581948645026, 0.8690258255251392, 1.4353495519534096, 1.7008629905310861, 1.6406255564489203, 1.2979379386679237, 0.7753132190763634, 0.21283075970549525, -0.24182236230374868, -0.4654274959494609, -0.38660221829158414, -0.002444755469111515, 0.6194260398257656, 1.3542679168738554, 2.0465437582639034, 2.5437605294275363, 2.7305597268009207, 2.555486569461605, 2.0442092179784837, 1.2957369454574956, 0.4618471464631275, -0.28629565226886444, -0.7972923895770833, -0.9757767657300582, -0.8073815674209128, -0.366127424240974, 0.1983903096782807, 0.6922161169966693, 0.9206024425784455, 0.7347707069760082, 0.07147809272482003, -1.0239690751781527, -2.39744895306156, -3.809994135742782, -4.982214741768515, -5.650693105318722, -5.624811536899586, -4.831808581902857, -3.3398348184134568, -1.35307072506061, 0.8212766573692124, 2.8282753224899317, 4.332097710889853, 5.080839526235435, 4.9558739100399025, 3.9952825744897917, 2.3862250566139815, 0.4276304177180809, -1.5290926231811346, -3.1489283076588848, -4.177278766524542, -4.48582895362727, -4.090981235906097, -3.1416636740066854, -1.8800600367039055, -0.5846966395226202, 0.49098743188413374, 1.1708009019100378, 1.3874124604653588, 1.1872004197684778, 0.7085391799118069, 0.13995393573056675, -0.33085819478893524, -0.5643215185368413, -0.5011074031784163, -0.17174364271947448, 0.31776078365095, 0.8196005486054414, 1.187636805960077, 1.318764183213457, 1.1810723171491386, 0.8213621899433048, 0.3502013769486786, -0.09118764839073418, -0.37292758831735867, -0.4155761560738806, -0.21516159733950344, 0.15326947784060074, 0.5551939971582837, 0.8344203017302714, 0.8590461188158797, 0.5627685490031672, -0.030502011953326316, -0.806663723927633, -1.5875366183715172, -2.1773264861794495, -2.417714260801235, -2.2367561611889233, -1.6775634607651502, -0.897370720795233, -0.13504576126093665, 0.34650893374464825, 0.32946076436063215, -0.2958845392272358, -1.4911075471371722, -3.0648432129434524, -4.706707026485389, -6.0537743345046655, -6.774704955496351, -6.651335170301474, -5.637238388553742, -3.877671011444953, -1.6844061490441118, 0.5299730228226225, 2.3434746057346567, 3.420132139651626, 3.58629857506, 2.8689464622443013, 1.4862994182594857, -0.20709614909105475, -1.807339923975897, -2.9585725801408476, -3.4365325069175863, -3.1975523761800093, -2.381147001002143, -1.266281754263366, -0.1933174050391006, 0.5276133495332692, 0.6977392157157774, 0.2792663043323571, -0.5989867127945826, -1.6805843854416396, -2.653850108654662, -3.2375762835083495, -3.256699243564591, -2.6875979088619877, -1.6612116868589906], 'positive_zeros': ['1.56338114816078794461764717030388', '3.84430976729850263897040642134389', '5.23186605284252143871694187634843', '6.76062110219825691660503441894212', '7.35396844672096316495025399900341', '8.566976238368070669968957406058001', '9.038024259879159491343031711112894', '10.46550260505941380842995120044436', '11.36528768435996488363943699397371', '13.12542196275629208009953813291552'], 'prelabel': '2-14e2-196.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.251026730176896, 'root_angle': 0.04387260122531599, 'root_number': '0.9622458532176444 + 0.272181773756891*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0438726012253', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.56338114816078794461764717030', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.84430976729850263897040642134', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.23186605284252143871694187635', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.5650678796170963, 'bad_primes': [2, 7], 'central_character': '196.103', 'conductor': 196, 'conductor_radical': 14, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/196/2/p/a/103/11'], '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': '2-14e2-196.103-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': '2-14e2-196.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.251026730176896, 'root_angle': 0.04387260122531599, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.56338114816078794461764717030', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1981821050851521278223292517828', 'Lhash_array': ['1981821050851521278223292517828'], 'factors': ['2-14e2-196.103-c1-0-6'], 'label': '2-14e2-196.103-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/196/2/p/a/103/11'}