-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1384143029446231245448346567622', 'a10': 0, 'a2': 1, 'a3': 1, 'a4': -1, 'a5': 0, 'a6': 1, 'a7': 3, 'a8': -3, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16.568958419415686, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1]], [83, [1, -1]]], 'bad_primes': [5, 83], 'central_character': '2075.1', 'coefficient_field': '1.1.1.1', 'conductor': 2075, 'conductor_radical': 415, 'degree': 2, 'euler_factors': [[1, -1, 2], [1, -1, 3], [1], [1, -3, 7], [1, -3, 11], [1, -6, 13], [1, 5, 17], [1, -2, 19], [1, -4, 23], [1, 7, 29], [1, -5, 31], [1, -11, 37], [1, 2, 41], [1, -8, 43], [1, 0, 47], [1, 6, 53], [1, -5, 59], [1, -5, 61], [1, -2, 67], [1, -2, 71], [1, 0, 73], [1, -14, 79], [1, -1], [1, 0, 89], [1, -8, 97], [1, 6, 101], [1, -4, 103], [1, -18, 107], [1, 17, 109], [1, 15, 113]], 'euler_factors_factorization': [[[[1, -1, 2], 1]], [[[1, -1, 3], 1]], [1], [[[1, -3, 7], 1]], [[[1, -3, 11], 1]], [[[1, -6, 13], 1]], [[[1, 5, 17], 1]], [[[1, -2, 19], 1]], [[[1, -4, 23], 1]], [[[1, 7, 29], 1]], [[[1, -5, 31], 1]], [[[1, -11, 37], 1]], [[[1, 2, 41], 1]], [[[1, -8, 43], 1]], [[[1, 0, 47], 1]], [[[1, 6, 53], 1]], [[[1, -5, 59], 1]], [[[1, -5, 61], 1]], [[[1, -2, 67], 1]], [[[1, -2, 71], 1]], [[[1, 0, 73], 1]], [[[1, -14, 79], 1]], [[[1, -1], 1]], [[[1, 0, 89], 1]], [[[1, -8, 97], 1]], [[[1, 6, 101], 1]], [[[1, -4, 103], 1]], [[[1, -18, 107], 1]], [[[1, 17, 109], 1]], [[[1, 15, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 59, 'label': '2-2075-1.1-c1-0-59', 'leading_term': '3.01821673942761025200181804418000000000000000000000000000000000000000000000000000000000000', '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/2075/2/a/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [3.01821673942761, 3.011592889094151, 2.9915356592749096, 2.957502587902563, 2.908636974415461, 2.8438350514819537, 2.7618327950853305, 2.6613064427838777, 2.540980560604975, 2.399737845186755, 2.2367255557173626, 2.05145432242699, 1.8438859060284951, 1.6145071875672155, 1.3643882197969046, 1.0952225875377015, 0.8093486505001192, 0.5097505309297631, 0.2000380086887507, -0.11559516488872354, -0.4324346027263565, -0.7453298343875168, -1.0487990626090327, -1.3371524664338879, -1.6046317036280007, -1.8455625574553471, -2.0545169786325044, -2.226480126339683, -2.3570174476882215, -2.4424363878736166, -2.479937026361606, -2.4677458174392775, -2.4052267009460366, -2.292964159187187, -2.132813339342218, -1.9279131385561004, -1.6826591528970365, -1.402634602542744, -1.094498734297107, -0.7658337287800144, -0.4249527536156862, -0.0806734474553606, 0.2579372722062697, 0.5818396811111749, 0.8823102765296539, 1.1512335566956844, 1.381385976522106, 1.566701104345315, 1.702505020211722, 1.7857114606733528, 1.814967143808597, 1.7907390976711683, 1.7153376413620833, 1.5928708848107052, 1.4291291544141569, 1.2314005303373514, 1.0082215934005168, 0.7690704067788012, 0.524011572052651, 0.28330576762969395, 0.05699836850185402, -0.14549656458706303, -0.3157995616426544, -0.44693854635642505, -0.5336738187072426, -0.5727590628502645, -0.5631242163362331, -0.505968785626296, -0.4047576222132058, -0.2651151676911452, -0.09461858425704184, 0.09750517127652428, 0.3007686009309785, 0.5038850364252926, 0.6952838510641077, 0.8636578041752225, 0.9985182149684009, 1.0907320810446568, 1.1330148254955315, 1.1203531652381258, 1.0503346761516639, 0.9233639610556764, 0.7427498143327748, 0.5146532685153277, 0.24789269023001453, -0.04639110039771861, -0.35519968996372525, -0.6642550139063654, -0.958667056266527, -1.2236623797708164, -1.4453401073470555, -1.6114189645910446, -1.7119376527403782, -1.7398713126405372, -1.6916292362106236, -1.5674032631670025, -1.3713423487338783, -1.1115363859805585, -0.7998012048557483, -0.45126635780275487, -0.08377738214470497, 0.28286579996473127, 0.6278033456955006, 0.9301036348745954, 1.1697993563099838, 1.3289213081280677, 1.3924775846626818, 1.3493263439647956, 1.1928935890600203, 0.9216933098819691, 0.5396157332019931, 0.055959983977608825, -0.5148002896140675, -1.1535164101380904, -1.8371135495717084, -2.539559709525641, -3.233012977973641, -3.889094420491261, -4.480225528274472, -4.980963646008798, -5.36926665863558, -5.6276196794347415, -5.743961616554191, -5.712358164548974, -5.533379632974643, -5.214156554797926, -4.768102511744824, -4.214311231444206, -3.57665281501313, -2.8826109582684927, -2.1619182559035357, -1.445059209026041, -0.7617195933278785, -0.13926575722787932, 0.39866221221836107, 0.8333638671616955, 1.1520277086063901, 1.3483590590466237, 1.4228460186011842, 1.38264270644412, 1.241070415455207, 1.0167592929638793, 0.7324744438375463, 0.4136896707648265, 0.08698822904753174, -0.221618066594209, -0.4883531210824394, -0.6932246356911279, -0.821360915700599, -0.8640516203576495, -0.8194232632029057, -0.6927004154096202, -0.4960271884331, -0.24784936235736724, 0.02811600250199063, 0.30427105466810345, 0.5508122086548966, 0.7375950520850182, 0.8360804056230347, 0.8212450634391116, 0.6733398196389145, 0.3793835659141796, -0.0657046511077245, -0.6584143069217157, -1.386446788692774, -2.2290388323608554, -3.157800425739816, -4.138030246555963, -5.130441840939252, -6.093207249950987, -6.9842033803930175, -7.763331541519967, -8.394773311598163, -8.849046889368834, -9.10473745649103, -9.149792436334469, -8.982296978420534, -8.61067515450729, -8.053296456771397, -7.337503185057437, -6.498109976389334, -5.575459815056824, -4.613149230112326, -3.655557159016219, -2.745325634126687, -1.9209450237286056, -1.2145915870661732, -0.6503507452805881, -0.24293649801157188, 0.0030128289381153883, 0.09301799788511916, 0.04221581732124329, -0.12577634591436823, -0.3805166815933093, -0.6868103525976571, -1.0070639193327637, -1.303771888975706, -1.541975608199048, -1.6915361991715938, -1.7290751062403855, -1.639457388368692, -1.4167228150872135, -1.0644061778283147, -0.5952286331134257, -0.030183665614976356, 0.602918410069965, 1.2713473415409517, 1.9396616770338506, 2.572079046484342, 3.1348471264604925, 3.5984548638849443, 3.939534989819554, 4.1423306010819205, 4.199629165999895, 4.11310463025784, 3.893049774861602, 3.557523708741775, 3.130980346072898, 2.642480003885584, 2.123615248187637, 1.6063017055398412, 1.1205932891373538, 0.6926784831591488, 0.34320013714331615, 0.08601662553661849, -0.07251102081565661, -0.13366089925973812, -0.1059186754391669, -0.004013458931088217, 0.15249809016725976, 0.3409846609204731, 0.5376901184814901, 0.719725496280192, 0.8669455447290803, 0.9635615379736364, 0.9993629078767254, 0.9704512096153064, 0.879428644068357, 0.735026954755433, 0.551207647069614, 0.3458076377484749, 0.13884221903725152, -0.049393441179483216, -0.200264600031054, -0.2986134829023702, -0.33429386737219247, -0.30328579459352634, -0.208284375734415, -0.0586978538721784, 0.1299624785140818, 0.3372678488599101, 0.539551652063894, 0.7119582430496886, 0.8307012519512859, 0.8753489539626654, 0.8309453799896875, 0.6897821205970016], 'positive_zeros': ['1.09189632316430757900963074575194', '2.41615676868067838581180557878323', '3.53133508802941266584945160071428', '4.13105076781702502762968049773287', '4.97148776811947809940547323320129', '5.87263406714637014971627456812711', '6.51003986895949489621827706153873', '7.80720406011570304437105683036266', '8.453475283691595638097668301696343', '9.017571364405704341140281754031679'], 'prelabel': '2-2075-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.070498546789532, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1310596821514859464, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.09189632316430757900963074575', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.41615676868067838581180557878', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.53133508802941266584945160071', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 16.568958419415686, 'bad_primes': [5, 83], 'central_character': '1.1', 'conductor': 2075, 'conductor_radical': 415, 'degree': 2, 'dirichlet_coefficients': [1, 1, 1, -1, 0, 1, 3, -3, -2, 0, 3, -1, 6, 3, 0, -1, -5, -2, 2, 0, 3, 3, 4, -3, 0, 6, -5, -3, -7, 0, 5, 5, 3, -5, 0, 2, 11, 2, 6, 0, -2, 3, 8, -3, 0, 4, 0, -1, 2, 0, -5, -6, -6, -5, 0, -9, 2, -7, 5, 0, 5, 5, -6, 7, 0, 3, 2, 5, 4, 0, 2, 6, 0, 11, 0, -2, 9, 6, 14, 0, 1, -2, 1, -3, 0, 8, -7, -9, 0, 0, 18, -4, 5, 0, 0, 5, 8, 2, -6, 0], 'euler11': [1, -3, 11], 'euler13': [1, -6, 13], 'euler17': [1, 5, 17], 'euler19': [1, -2, 19], 'euler2': [1, -1, 2], 'euler23': [1, -4, 23], 'euler29': [1, 7, 29], 'euler3': [1, -1, 3], 'euler31': [1, -5, 31], 'euler37': [1, -11, 37], 'euler41': [1, 2, 41], 'euler43': [1, -8, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, 6, 53], 'euler59': [1, -5, 59], 'euler61': [1, -5, 61], 'euler67': [1, -2, 67], 'euler7': [1, -3, 7], 'euler71': [1, -2, 71], 'euler73': [1, 0, 73], 'euler79': [1, -14, 79], 'euler83': [1, -1, 0], 'euler89': [1, 0, 89], 'euler97': [1, -8, 97], 'euler_factors': [[1, -1, 2], [1, -1, 3], [1, 0, 0], [1, -3, 7], [1, -3, 11], [1, -6, 13], [1, 5, 17], [1, -2, 19], [1, -4, 23], [1, 7, 29], [1, -5, 31], [1, -11, 37], [1, 2, 41], [1, -8, 43], [1, 0, 47], [1, 6, 53], [1, -5, 59], [1, -5, 61], [1, -2, 67], [1, -2, 71], [1, 0, 73], [1, -14, 79], [1, -1, 0], [1, 0, 89], [1, -8, 97]], 'index': 59, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/2075/d', 'ModularForm/GL2/Q/holomorphic/2075/2/a/d/1/1', 'ModularForm/GL2/Q/holomorphic/2075/2/a/d'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-2075-1.1-c1-0-59', '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': '2-2075-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.070498546789532, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1310596821514859464, 'z1': {'__RealLiteral__': 0, 'data': '1.09189632316430757900963074575', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20685539
{'Lhash': '1384143029446231245448346567622', 'Lhash_array': ['1384143029446231245448346567622'], 'label': '2-2075-1.1-c1-0-59', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2075/2/a/d'}
-
id: 24555715
{'Lhash': '1384143029446231245448346567622', 'Lhash_array': ['1384143029446231245448346567622'], 'label': '2-2075-1.1-c1-0-59', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2075/2/a/d/1/1'}
-
id: 97748
{'Lhash': '1310596821514859464', 'Lhash_array': ['1310596821514859464'], 'label': '2-2075-1.1-c1-0-59', 'type': 'ECQ', 'url': 'EllipticCurve/Q/2075/d'}