-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1490649928621007156203015346325', 'a10': [7.3484692283495345, 0.0], 'a2': [0.0, -1.4142135623730951], 'a3': [0.0, 0.0], 'a4': [-2.0, 0.0], 'a5': [0.0, 5.196152422706632], 'a6': [0.0, 0.0], 'a7': [6.3484692283495345, 0.0], 'a8': [0.0, 2.8284271247461903], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.41418028263681, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.4142135623730951]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '162.161', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '2206230022785775429395082551437', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.4142135623730951]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -5.196152422706632], [-25.0, 0]], [[1.0, 0], [-6.3484692283495345, 0], [49.0, 0]], [[1.0, 0], [0, -9.438793109825918], [-121.0, 0]], [[1.0, 0], [-19.69693845669907, 0], [169.0, 0]], [[1.0, 0], [0, -1.9070234711746934], [-289.0, 0]], [[1.0, 0], [-4.696938456699068, 0], [361.0, 0]], [[1.0, 0], [0, 9.438793109825918], [-529.0, 0]], [[1.0, 0], [0, 3.2891289515319384], [-841.0, 0]], [[1.0, 0], [41.0454076850486, 0], [961.0, 0]], [[1.0, 0], [-17.30306154330093, 0], [1369.0, 0]], [[1.0, 0], [0, -61.828911081662135], [-1681.0, 0]], [[1.0, 0], [-0.9545923149513971, 0], [1849.0, 0]], [[1.0, 0], [0, 14.1100275417151], [-2209.0, 0]], [[1.0, 0], [0, -9.535117355873467], [-2809.0, 0]], [[1.0, 0], [0, 91.52739589149714], [-3481.0, 0]], [[1.0, 0], [75.0908153700972, 0], [3721.0, 0]], [[1.0, 0], [-30.954592314951398, 0], [4489.0, 0]], [[1.0, 0], [0, 85.9026497240206], [-5041.0, 0]], [[1.0, 0], [96.0908153700972, 0], [5329.0, 0]], [[1.0, 0], [-29.74234614174767, 0], [6241.0, 0]], [[1.0, 0], [0, 87.90599744124285], [-6889.0, 0]], [[1.0, 0], [0, -41.376570889557954], [-7921.0, 0]], [[1.0, 0], [-95.87856919689348, 0], [9409.0, 0]], [[1.0, 0], [0, 157.9312171590009], [-10201.0, 0]], [[1.0, 0], [-29.13622305514581, 0], [10609.0, 0]], [[1.0, 0], [0, 171.8052994480412], [-11449.0, 0]], [[1.0, 0], [-116.27244611029161, 0], [11881.0, 0]], [[1.0, 0], [0, 202.26464750136844], [-12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-162-3.2-c2-0-3', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/162/3/b/a/161/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.5399782951550798, 1.4883365197589893, 1.4180778162596621, 1.3266001945321177, 1.2104888933751463, 1.0658447582018338, 0.8886875619166458, 0.6754066530473456, 0.42323360658885256, 0.13071367518019508, -0.20184704395323755, -0.5719839186764691, -0.9747541216764493, -1.40252667423434, -1.844915254010429, -2.2888852604932963, -2.71906127873554, -3.118251526541392, -3.4681921377399894, -3.750496716806827, -3.947776477260621, -4.044874910710222, -4.030140225135015, -3.896640975318885, -3.6432177926010065, -3.2752592621417214, -2.805094831305678, -2.2519135869345175, -1.6411453347755007, -1.0032790250322283, -0.37214125383530977, 0.21728896798838937, 0.7313983026032684, 1.1406087733833339, 1.4219777782378933, 1.5614834732265828, 1.5557484276191955, 1.4129775032918392, 1.1529355799163272, 0.8058656537273593, 0.410343483981256, 0.010173740917907735, -0.3494557956799385, -0.62624325114156, -0.7850663167377459, -0.8018567159508765, -0.6666107529874162, -0.38514061516156023, 0.02072861702348147, 0.5146656515402257, 1.0490135969288843, 1.5694196463923389, 2.0204998052071486, 2.351965317606579, 2.5245311640624326, 2.514893042251767, 2.3191099884662916, 1.9538681507543885, 1.4553190306402186, 0.8754632212779282, 0.27635855823091476, -0.2772674805400239, -0.7261677449451968, -1.024486734324309, -1.1463816363004742, -1.0903863836236447, -0.8807744112459437, -0.5655187289706823, -0.21087598623865642, 0.10691659764938416, 0.3119072398336431, 0.3393892589192336, 0.14608715879774, -0.2819074901499264, -0.9247293689795535, -1.72874595703938, -2.6113082068758606, -3.4699308105649256, -4.1949351899923935, -4.6840232678485805, -4.8568619137503015, -4.667618003171833, -4.113532763268166, -3.238062268722421, -2.1277959651929894, -0.9032136301493948, 0.29576148307905314, 1.327640537681324, 2.06830110238087, 2.4283088704159588, 2.3660588553250514, 1.8946518544649291, 1.081250117251099, 0.038719727923878414, -1.0894845196992742, -2.149176887178422, -2.997227038229017, -3.522061438577461, -3.6597506893987033, -3.4031330928028227, -2.802430749135812, -1.95710535447778, -1.0000805492486242, -0.07670514009350385, 0.6782636930846293, 1.16197986235966, 1.3196484035293854, 1.1527835517802392, 0.7181374611537485, 0.11738776092054855, -0.5207638487417484, -1.0631053869304625, -1.3952173353072603, -1.4415358163365573, -1.1786422660702915, -0.639375943935869, 0.09304854866892819, 0.8999645261728233, 1.6486185556423356, 2.216165216233424, 2.5119311785301695, 2.493829902278568, 2.1758192598625197, 1.6249113554510295, 0.948182870227163, 0.27213956923499133, -0.28170333197571784, -0.62035444035372, -0.6973927938486447, -0.5218938600061493, -0.15630727968204575, 0.29650222046817687, 0.7146724805795595, 0.9830749650107503, 1.0182141212860827, 0.7871475049567855, 0.3163158326119964, -0.3119168594813612, -0.9747757112451535, -1.5339104908315166, -1.8647805003777052, -1.8846573012518457, -1.573319019624754, -0.9817329951673774, -0.22627208060432244, 0.5311274265426825, 1.1135390226407063, 1.3646441422577564, 1.1823250795041114, 0.5432771047421944, -0.48684777679139246, -1.7605692410428635, -3.072399452258618, -4.1953567775930685, -4.923419184384501, -5.111672638110551, -4.706042251729868, -3.7562910475855382, -2.4091299995029907, -0.8822049178346972, 0.5763709881118523, 1.7351940483856259, 2.424129934742039, 2.5672211572440755, 2.1970719980095197, 1.4474857737377873, 0.5255368564415102, -0.33147196739718354, -0.9054877222281026, -1.0434598575260232, -0.689826090324711, 0.10116998922695133, 1.1760880271691245, 2.3137905742120726, 3.2713631236986775, 3.834868525841665, 3.8642453628125266, 3.3228374218652, 2.2852793526518353, 0.9220853516365417, -0.5356992637424807, -1.8441148966260177, -2.7958564044614613, -3.261092005713699, -3.2108125889463097, -2.7179151234754424, -1.9362196002973375, -1.0625636059767278, -0.29088693495834417, 0.23105852261541315, 0.43246902137874427, 0.3308431659518993, 0.021687136818148434, -0.35051172795070423, -0.632654346639913, -0.7046409236557397, -0.5118345962364259, -0.08022272898769915, 0.48963173866793347, 1.0484996257246135, 1.4379079991112622, 1.5332197807571237, 1.2793895322803044, 0.7100031733028602, -0.05581775250656854, -0.8386355381838693, -1.4404497231483058, -1.6930541581082066, -1.501082101263836, -0.8687594698518303, 0.09690033093516853, 1.2080757184655164, 2.238667818797723, 2.9774754850270058, 3.2791290820522647, 3.1000486261361537, 2.510038274009732, 1.6759394497267168, 0.8206647820729708, 0.1672294373709053, -0.11851652767711847, 0.02802518784860705, 0.5509311968715098, 1.285063430264746, 1.996178929095709, 2.4407126638494434, 2.430783689168432, 1.888100159928094, 0.8726008750270663, -0.42253278750057904, -1.7097600676169045, -2.67177208654605, -3.0369035507120565, -2.6472595176622855, -1.5026272364881543, 0.23135226223021246, 2.2538722059515983, 4.192232519862756, 5.683349531476578, 6.45444199084291, 6.383716392163453, 5.526469316945121, 4.100263838697129, 2.432721451294091, 0.8845566628923551, -0.23350772213180962, -0.7298978305316411, -0.5709438273570964, 0.1195699219401084, 1.0990218537866479, 2.072186063414959, 2.7677668608747195, 3.005633184609524, 2.737911253320991, 2.054165854309338, 1.150423535052969, 0.27126058122189123], 'positive_zeros': ['1.17591545205960433921518015879119', '3.82741060615451024193347292958573', '5.12828783582401275524614668285668', '5.99430522267691183241930355741433', '7.56024006225782581850414484474030', '8.579326368995866687649677907974621', '9.050836290853121295207364771755172', '10.71807965055971911841354749620671', '11.62935106744404132143347949858796', '12.88625701652401042044577797249530'], 'prelabel': '2-162-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.100995069636483, 'root_angle': 2.9614245770195926e-61, 'root_number': '1.0 + 9.303589695325013e-61*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.000000000000000000000000000000000000000000000000000000000000148071228851', 'prec': 246}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.17591545205960433921518015879', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.82741060615451024193347292959', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.12828783582401275524614668286', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.41418028263681, 'bad_primes': [2, 3], 'central_character': '3.2', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/3/b/a/161/2'], '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': '2-162-3.2-c2-0-3', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-162-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.100995069636483, 'root_angle': 1.4807122885097963e-61, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.17591545205960433921518015879', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1490649928621007156203015346325', 'Lhash_array': ['1490649928621007156203015346325'], 'label': '2-162-3.2-c2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/3/b/a/161/2'}