-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2296549911139556230081083243663', 'a10': [8.310142873699929e-61, 9.084091523900877], 'a2': [-2.2407434478441743, 0.6004053972951761], 'a3': [0.7243682318597995, 1.5733056488401445], 'a4': [2.928393750386542, -1.6907089200788878], 'a5': [1.0135131191213242, -3.78248245469839], 'a6': [-2.567744572524927, -3.090459728056994], 'a7': [2.272258506127028, -0.6088498317114864], 'a8': [-2.265992246918014, 2.265992246918014], 'a9': [-1.9505813293446157, 2.27930526205074], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.934249703648981, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.7243682318597995, -1.5733056488401445]]], [13, [[1.0, 0], [-1.9957353492970094, 3.0028387261999843]]]], 'bad_primes': [3, 13], 'central_character': '117.83', 'coefficient_field': 'CDF', 'conductor': 117, 'conductor_radical': 39, 'conjugate': '1933290378915407597671801950686', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.2407434478441743, -0.6004053972951761], [1.7320508075688772, -1.0]], [[1.0, 0], [-0.7243682318597995, -1.5733056488401445]], [[1.0, 0], [-1.0135131191213242, 3.78248245469839], [-4.330127018922194, -2.5]], [[1.0, 0], [-2.272258506127028, 0.6088498317114864], [6.06217782649107, -3.5]], [[1.0, 0], [-0.6379345739725406, -2.3808042419703277], [-9.526279441628825, 5.5]], [[1.0, 0], [-1.9957353492970094, 3.0028387261999843]], [[1.0, 0], [-0.901010576289277, 0], [17.0, 0]], [[1.0, 0], [2.0700418092665154, -2.0700418092665154], [0, -19.0]], [[1.0, 0], [-1.5035067483824667, -2.6041500777211084], [-11.5, 19.91858428704209]], [[1.0, 0], [-2.195463893639251, -1.2675516699887255], [14.5, 25.11473670974872]], [[1.0, 0], [-1.9278767451376604, -0.5165730169663775], [26.846787517317598, 15.5]], [[1.0, 0], [7.885023350325017, 7.885023350325017], [0, 37.0]], [[1.0, 0], [0.8953507206357983, -3.3414943800062074], [-35.50704155516198, -20.5]], [[1.0, 0], [-5.1190069739527395, -2.9554600543951857], [21.5, 37.239092362730865]], [[1.0, 0], [-0.2590018415517266, -0.9666080319249477], [-40.703193977868615, 23.5]], [[1.0, 0], [0, -0.6353661187760926], [-53.0, 0]], [[1.0, 0], [5.54121112622844, 1.4847630463632624], [51.09549882328188, 29.5]], [[1.0, 0], [4.381949132979762, -7.589758534503337], [-30.5, -52.827549630850754]], [[1.0, 0], [8.849606196468653, 2.371244833677235], [58.023702053557386, 33.5]], [[1.0, 0], [7.93440686032896, 7.93440686032896], [0, 71.0]], [[1.0, 0], [-9.168877961268647, -9.168877961268647], [0, 73.0]], [[1.0, 0], [0.2042340394167179, -0.3537437329047801], [-39.5, -68.41600689897065]], [[1.0, 0], [3.6649433164496696, -0.9820186019485295], [71.88010851410841, -41.5]], [[1.0, 0], [10.087192293022394, -10.087192293022394], [0, -89.0]], [[1.0, 0], [0.7338248685366936, 2.7386716932364927], [-84.00446416709055, 48.5]], [[1.0, 0], [-0.4927434576407952, 0.8534567037310202], [-50.5, -87.4685657822283]], [[1.0, 0], [2.598075639626575, -1.4999996699134122], [51.5, -89.20061658979718]], [[1.0, 0], [0, 8.136246180920244], [-107.0, 0]], [[1.0, 0], [-3.0906686742288816, 3.0906686742288816], [0, -109.0]], [[1.0, 0], [-1.8757671977296484, 1.0829746965462825], [56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-117-117.83-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/117/2/z/b/83/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.669897070456274, 0.6705321770448683, 0.6743469352963786, 0.6797964570205731, 0.6844471370915219, 0.6852739165468842, 0.678950637859342, 0.6621112354503896, 0.6315887909514316, 0.5846510271052933, 0.5192480241349032, 0.43427863174860554, 0.3298716700754994, 0.2076688841751592, 0.07108930997096537, -0.0744507520468039, -0.22139153100586798, -0.35998819537348126, -0.4784037614136475, -0.5629626189578167, -0.5985839433021936, -0.5694042178454218, -0.45958500158926624, -0.25428640623852716, 0.05923067802338885, 0.4904285697076395, 1.04431502917573, 1.7203501642976615, 2.511534280891977, 3.403776421224488, 4.375638841631394, 5.398539088159337, 6.437468162365074, 7.452250899301135, 8.399334453844688, 9.234045085484608, 9.913205599310707, 10.397960008308704, 10.656612920486308, 10.667263641395351, 10.420003474736191, 9.918452759797434, 9.18044393265256, 8.237708568392861, 7.13449795091882, 5.925153847735631, 4.670742193764983, 3.434958776275557, 2.2796029987336692, 1.2599832949261587, 0.4206564325143104, -0.20809463132910858, -0.6126778959132458, -0.7972173324981405, -0.7830149895010672, -0.606424098637553, -0.3152671999584849, 0.03590733403911311, 0.3912962631488932, 0.6995014059879693, 0.9187872391691894, 1.0213546195638492, 0.9961258371216111, 0.8496768835729592, 0.605146240824504, 0.2991768915387858, -0.022815169181593938, -0.3125352303024205, -0.5251866586438285, -0.6255532939049986, -0.5930052203176236, -0.42473970351070056, -0.13675828162032982, 0.23765169178293874, 0.651846347899436, 1.0517534413083827, 1.3830922442773377, 1.5989578527212251, 1.666733263812861, 1.5733183115045193, 1.3278327291060201, 0.961249415359112, 0.5228121413346027, 0.07354133386858556, -0.32242747446305065, -0.6075591926939516, -0.7403378647837886, -0.7029766477585394, -0.5061463566898952, -0.18978570996839053, 0.18044355938801904, 0.5208888236353109, 0.7410286387906455, 0.7566241393124582, 0.5031303689403818, -0.05258273656254032, -0.9040576357301522, -2.0021086136869677, -3.2575745810189183, -4.550028275566141, -5.741636577196174, -6.69455252608123, -7.2895856342991125, -7.443551561694719, -7.122718012869694, -6.350164130961818, -5.205622165029195, -3.8173832435677313, -2.3469879181041966, -0.9685224424669373, 0.15476576534319483, 0.8932835875746804, 1.170010841596736, 0.9726128274103867, 0.35671532685260343, -0.560463033520875, -1.6155225051305915, -2.6213668160770123, -3.3936618493522723, -3.777473100910401, -3.6701477625829853, -3.0369697144840533, -1.9171289847891433, -0.4189704596772983, 1.294892672188548, 3.030449470883191, 4.589736062983417, 5.798704473287002, 6.531274723706427, 6.725917491702934, 6.392297579587718, 5.607100900043971, 4.499910655465003, 3.231601471819706, 1.9689108278012286, 0.8594183264902177, 0.011012160812195427, -0.5209296552937285, -0.7368220103229877, -0.6865115804704186, -0.4548783570546146, -0.14241023511152073, 0.15540407668302042, 0.3659099487649032, 0.45103679528756, 0.4109233178228567, 0.2790421243880443, 0.11018168255717012, -0.03589402750628986, -0.111392864566972, -0.09419720956444333, 0.004862723820308666, 0.14299503014428883, 0.2547386746208161, 0.2677541929677048, 0.12176247647595463, -0.2136087317276469, -0.726330694774045, -1.3581912765261683, -2.0114012127146057, -2.565110415185729, -2.8991515662929275, -2.920535618169051, -2.5872454749546, -1.923969681280688, -1.025641752343916, -0.04682839622558889, 0.8222403377261034, 1.3894075448691023, 1.4982214653082182, 1.062329195349739, 0.08957632954253524, -1.309751554314434, -2.9334116940555934, -4.5158353014700054, -5.770783245981516, -6.4409442061422855, -6.345640791607646, -5.417671249243464, -3.7218999646837223, -1.4512916817806696, 1.0998717446722295, 3.581594560440767, 5.644939723806696, 7.000005148019212, 7.464654495336887, 6.995050265277935, 5.692274801038034, 3.783713116009643, 1.5825763164560642, -0.5669496070898392, -2.3487519109075197, -3.527124136083138, -3.9828568155208917, -3.7267978569766202, -2.8890456875621697, -1.6867070309206293, -0.3772734725946682, 0.792688187731139, 1.6332075728201565, 2.0421141201008646, 2.016225659284706, 1.641338336995362, 1.064338027816582, 0.4544341675050306, -0.0374078574673246, -0.31171931754375076, -0.3393246600535206, -0.16206687391200722, 0.12388576188184483, 0.39746321164527115, 0.5472743120839372, 0.5026934507078792, 0.2537728475523001, -0.14491269678247717, -0.5874333481484534, -0.9434509608705097, -1.0922976223562149, -0.9557105855161281, -0.5209616862613198, 0.15165081730919622, 0.9392424267018539, 1.6826433068459867, 2.2225426166043314, 2.4369008813536563, 2.270538292257913, 1.7495046365126712, 0.9763874844994055, 0.10729639458532204, -0.6842249914739915, -1.2477721541023374, -1.4912513809087704, -1.401879568553592, -1.0475726413308977, -0.5580721552242544, -0.0902629395513161, 0.21371194292948778, 0.2648056642789805, 0.05167325139750397, -0.3555499179861894, -0.8242820791033675, -1.1974705689011511, -1.3414543530184964, -1.1914869769950183, -0.7824386579589993, -0.2550880950548899, 0.16608425910982139, 0.22078842977611376, -0.32299386000502944, -1.6030496188510492, -3.611067556190709, -6.168752931065036, -8.940274235314929, -11.481522273909665, -13.318201505101293, -14.03768127382232, -13.375533189728902], 'positive_zeros': ['1.81165844178678455103924968029934', '2.97951775036803070516497326470567', '6.32849185226057388628628728473833', '7.11260518813545481899740024844765', '8.240945338428186487694289612719430', '9.048305871941290891006053587852371', '10.39647051415069651888665537103441', '11.18966689120698934304052080258098', '11.86556846579138698335888656221741', '13.73023864220123120683254535369078'], 'prelabel': '2-117-117.83-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9665659334204681, 'root_angle': -0.126000906416339, 'root_number': '0.9226716418809019 - 0.3855866196703417*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0630004532082', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.81165844178678455103924968030', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.97951775036803070516497326471', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.32849185226057388628628728474', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.934249703648981, 'bad_primes': [3, 13], 'central_character': '117.83', 'conductor': 117, 'conductor_radical': 39, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/117/2/z/b/83/1'], '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': '2-117-117.83-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': '2-117-117.83-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9665659334204681, 'root_angle': -0.0630004532081695, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.81165844178678455103924968030', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2296549911139556230081083243663', 'Lhash_array': ['2296549911139556230081083243663'], 'label': '2-117-117.83-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/117/2/z/b/83/1'}