-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '738332051054939493833230384896', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [-2.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-5.196152422706632, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.145246147436753, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '1521.1', 'coefficient_field': 'CDF', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [5.0, 0]], [[1.0, 0], [5.196152422706632, 0], [7.0, 0]], [[1.0, 0], [0, 0], [11.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [17.0, 0]], [[1.0, 0], [3.4641016151377544, 0], [19.0, 0]], [[1.0, 0], [0, 0], [23.0, 0]], [[1.0, 0], [0, 0], [29.0, 0]], [[1.0, 0], [-8.660254037844387, 0], [31.0, 0]], [[1.0, 0], [6.928203230275509, 0], [37.0, 0]], [[1.0, 0], [0, 0], [41.0, 0]], [[1.0, 0], [-13.0, 0], [43.0, 0]], [[1.0, 0], [0, 0], [47.0, 0]], [[1.0, 0], [0, 0], [53.0, 0]], [[1.0, 0], [0, 0], [59.0, 0]], [[1.0, 0], [-13.0, 0], [61.0, 0]], [[1.0, 0], [-12.12435565298214, 0], [67.0, 0]], [[1.0, 0], [0, 0], [71.0, 0]], [[1.0, 0], [1.7320508075688772, 0], [73.0, 0]], [[1.0, 0], [-13.0, 0], [79.0, 0]], [[1.0, 0], [0, 0], [83.0, 0]], [[1.0, 0], [0, 0], [89.0, 0]], [[1.0, 0], [19.05255888325765, 0], [97.0, 0]], [[1.0, 0], [0, 0], [101.0, 0]], [[1.0, 0], [-13.0, 0], [103.0, 0]], [[1.0, 0], [0, 0], [107.0, 0]], [[1.0, 0], [8.660254037844387, 0], [109.0, 0]], [[1.0, 0], [0, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-39e2-1.1-c1-0-5', 'leading_term': '0.72244514603916392932376118539024', '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/1521/2/a/i/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.7224451460391639, 0.715739791837118, 0.6955242273784511, 0.66150882759283, 0.6132398283182605, 0.5501405440817285, 0.4715650136227259, 0.37686070685459927, 0.2654367483024093, 0.13683424415282647, -0.009204369566342454, -0.1726696268153393, -0.35322524237735753, -0.5501561505511511, -0.7623260192329694, -0.9881456845800348, -1.2255537910854166, -1.4720107733559922, -1.724507150841461, -1.9795869026337236, -2.2333864310193596, -2.481689302006429, -2.7199965677492264, -2.943612034868807, -3.14774135441474, -3.3276032881634587, -3.478550970060172, -3.596200451519461, -3.6765633175602295, -3.71617971105436, -3.712247728698391, -3.6627448780455403, -3.5665371318606893, -3.423471103412123, -3.2344450097427124, -3.0014544005674835, -2.727609113863818, -2.417118574851997, -2.0752433754455586, -1.7082120416601598, -1.3231029947770987, -0.9276929088754678, -0.5302739264946705, -0.1394434734948462, 0.23612833338071074, 0.5879475175940312, 0.9079540981257962, 1.188780889892619, 1.4240045357257358, 1.6083796965911596, 1.7380472788483539, 1.8107078692661345, 1.825752196783644, 1.7843414480685098, 1.689431620815055, 1.5457377782411077, 1.3596360287206664, 1.1390032392374212, 0.892996829760068, 0.6317794050537746, 0.3661953686430757, 0.10740893205348823, -0.13348502013146973, -0.34586402214030826, -0.5199805762289927, -0.647348844907251, -0.7210999228376664, -0.7362904908404981, -0.6901506612229911, -0.5822584720108703, -0.4146307505026222, -0.19172288829135434, 0.0796666332483702, 0.39058746625722707, 0.7302209747495986, 1.0862488029486457, 1.4452951851912132, 1.7934281271984016, 2.1167014013904026, 2.4017167114205336, 2.6361835418409916, 2.809453242213684, 2.9130038939342633, 2.940853527546274, 2.8898813104783176, 2.7600393757907273, 2.5544419299043115, 2.2793230328163725, 1.943859815660167, 1.5598636769324339, 1.1413479387859142, 0.7039862856626983, 0.26448177631513425, -0.16012895374339756, -0.5532077544813785, -0.8992519407371025, -1.1846033497783934, -1.3980965917572232, -1.5316150788401746, -1.5805264108644124, -1.5439731395176575, -1.4250006871220817, -1.230511047708191, -0.9710385711473379, -0.660352296153306, -0.3148975853987354, 0.04690216761229382, 0.4054556439402026, 0.7408911096714131, 1.0339820392654542, 1.2670683788475394, 1.4249297271495758, 1.4955675353346325, 1.4708563678285083, 1.347029265050337, 1.1249691402279405, 0.8102866585037146, 0.4131748259465196, -0.05195888178355384, -0.567071097479089, -1.1112493859869224, -1.6616349102174504, -2.1944598920408436, -2.686151960450554, -3.114452817333622, -3.4594965033267115, -3.7047931102530294, -3.838067126396171, -3.851905637461907, -3.7441801161188817, -3.518216154615826, -3.182697741497178, -2.751305964523744, -2.2421056710821814, -1.6767069249768454, -1.0792403483625352, -0.475195945577332, 0.10981684186339323, 0.6513248098566307, 1.1271972977877838, 1.5187394052117684, 1.8116132353907213, 1.9965364138796493, 2.069718205333005, 2.033007044167613, 1.8937385284264106, 1.6642891067445202, 1.361356943598952, 1.0050068745644203, 0.6175300762385691, 0.22218025934179347, -0.1581438491888952, -0.5021957741053161, -0.7915842533716637, -1.0118119551215266, -1.1530882194320682, -1.210866028321922, -1.1860684792976557, -1.0849874600710987, -0.9188560475277049, -0.7031153257232629, -0.45641472720713566, -0.1994015526940735, 0.04663100397972333, 0.26115808643650035, 0.4258149553511897, 0.525681030899565, 0.5503753863496198, 0.49489228094004817, 0.360119220050618, 0.15299772450262475, -0.11369247456192744, -0.4219228742741874, -0.7493537023106871, -1.0705722267902456, -1.3585652030059867, -1.5863428730322564, -1.728620576277443, -1.763458034249612, -1.6737562469564715, -1.4485178452848084, -1.0837884851048183, -0.5832138858075026, 0.041831487316974336, 0.7725635085424044, 1.5835482901904556, 2.4438693562919016, 3.318643369420059, 4.170803474790758, 4.963051511025938, 5.659868115467587, 6.229464002099066, 6.645556911864318, 6.888867008548258, 6.948238462670831, 6.821315850520426, 6.514729628259047, 6.04377383158981, 5.431589572066005, 4.707897989862818, 3.9073541981805135, 3.0676176339705274, 2.227252545647251, 1.4235838527094105, 0.690637463233591, 0.05728996132117315, -0.4542594895987726, -0.8296015004333739, -1.0627449942133873, -1.1562239126139284, -1.1206768785135792, -0.973928080135981, -0.7396296447266468, -0.4455542018650482, -0.12164929909964872, 0.20201874991323054, 0.4972962736383064, 0.7398146748724034, 0.9105795959618814, 0.9971707977181633, 0.994472240230193, 0.9048830020823423, 0.7379944641986094, 0.5097553374270125, 0.24118121912841067, -0.04330295885633186, -0.3177731740091445, -0.5568362529130101, -0.7376367876637313, -0.8416982449857663, -0.8564652393555588, -0.776433010514845, -0.6037773767057427, -0.34843209527171315, -0.027598445614200932, 0.3352885826538687, 0.7120745642418191, 1.071782597483819, 1.38276650928213, 1.6149734916183078, 1.742158835756118, 1.743895681822431, 1.6072339107288867, 1.327883900650533, 0.9108315456304537, 0.37032872497819097, -0.2707541805353915, -0.9821829773139896, -1.728147956420226, -2.469473679606664, -3.1661067075589515, -3.7797157279573215, -4.276227690335662, -4.628124815525625, -4.816340853054941, -4.831619984740083, -4.675236766612259], 'positive_zeros': ['0.58244129014888587342252076828357', '2.54093920856658529073826340380292', '3.59965430816273419096247497725435', '4.20249564433908539379775542484639', '5.42673022080874236713083437174242', '6.20338026813584923889916123381903', '6.90785819662818302222573672090319', '8.016079466379376999417096621776921', '8.822791374383340678835143040773690', '9.539231180083738508171994864326965'], 'prelabel': '2-39e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4850030340642104, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.58244129014888587342252076828', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.54093920856658529073826340380', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.59965430816273419096247497725', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 12.145246147436753, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/2/a/i/1/1'], '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': '2-39e2-1.1-c1-0-5', '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': '2-39e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4850030340642104, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.58244129014888587342252076828', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '738332051054939493833230384896', 'Lhash_array': ['738332051054939493833230384896'], 'label': '2-39e2-1.1-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/2/a/i/1/1'}