Table lfunc_lfunctions
L-functions
{'Lhash': '2144165641489502102497440819383', 'a10': -2, 'a2': -1, 'a3': 2, 'a4': 1, 'a5': 2, 'a6': -2, 'a7': 1, 'a8': -1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.241926322063985, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [1, 1]], [7, [1, -1]], [29, [1, 1]]], 'bad_primes': [2, 7, 29], 'central_character': '406.1', 'coefficient_field': '1.1.1.1', 'conductor': 406, 'conductor_radical': 406, 'degree': 2, 'euler_factors': [[1, 1], [1, -2, 3], [1, -2, 5], [1, -1], [1, -4, 11], [1, 2, 13], [1, 4, 17], [1, -2, 19], [1, 0, 23], [1, 1], [1, 2, 31], [1, -2, 37], [1, -8, 41], [1, 8, 43], [1, -6, 47], [1, -6, 53], [1, 4, 59], [1, -4, 61], [1, 4, 67], [1, -8, 71], [1, 12, 73], [1, 12, 79], [1, 0, 83], [1, -4, 89], [1, -4, 97], [1, 12, 101], [1, 16, 103], [1, 12, 107], [1, 14, 109], [1, -18, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [[[1, -2, 3], 1]], [[[1, -2, 5], 1]], [[[1, -1], 1]], [[[1, -4, 11], 1]], [[[1, 2, 13], 1]], [[[1, 4, 17], 1]], [[[1, -2, 19], 1]], [[[1, 0, 23], 1]], [[[1, 1], 1]], [[[1, 2, 31], 1]], [[[1, -2, 37], 1]], [[[1, -8, 41], 1]], [[[1, 8, 43], 1]], [[[1, -6, 47], 1]], [[[1, -6, 53], 1]], [[[1, 4, 59], 1]], [[[1, -4, 61], 1]], [[[1, 4, 67], 1]], [[[1, -8, 71], 1]], [[[1, 12, 73], 1]], [[[1, 12, 79], 1]], [[[1, 0, 83], 1]], [[[1, -4, 89], 1]], [[[1, -4, 97], 1]], [[[1, 12, 101], 1]], [[[1, 16, 103], 1]], [[[1, 12, 107], 1]], [[[1, 14, 109], 1]], [[[1, -18, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 10236834, 'index': 3, 'label': '2-406-1.1-c1-0-3', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/406/2/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [1.6960278446405448, 1.6967872339828647, 1.6974097450076535, 1.6932307290137159, 1.677384554888085, 1.6418917316512176, 1.578807805655792, 1.4813067917314213, 1.344653179813279, 1.1670478648356686, 0.950323667152283, 0.7004405600029459, 0.4277087297433952, 0.14665905288490533, -0.1245109705729603, -0.36496202839244585, -0.552713224688086, -0.6665682209178299, -0.6883557852374153, -0.6053100126170872, -0.41235911154955357, -0.11405115807361475, 0.2741704636163315, 0.7256124420110331, 1.203114058156409, 1.661090589835483, 2.048834474725661, 2.3149196129672367, 2.4123931735162905, 2.3042882498633444, 1.9688717356985443, 1.403976762035368, 0.6297765038748302, -0.3105520346091338, -1.3526474003493099, -2.4153844336919845, -3.40770525812561, -4.2373396016245115, -4.820585635244505, -5.092082556983224, -5.013377521562866, -4.5791059943687635, -3.8197837135476123, -2.800546270347548, -1.615640889658736, -0.3790230311678362, 0.7880320579633626, 1.770906160458892, 2.4754707177026365, 2.8399238144816703, 2.8429188227133877, 2.5066737097356713, 1.8943793529122195, 1.1020070930244714, 0.24544293087020128, -0.5553773082279072, -1.1931159036788117, -1.5880156801707384, -1.698907256921146, -1.5284483528329242, -1.1216410988813135, -0.5577179837737892, 0.06342329205133415, 0.6381035411905649, 1.076290654955768, 1.3166021451864838, 1.3362227056522098, 1.1538776079003645, 0.8251792116659998, 0.4310282949354058, 0.06106614163092738, -0.20481002927604636, -0.3133475066588062, -0.24986500278571483, -0.04260711078638419, 0.24172861477073926, 0.5108702065407842, 0.6661275076930125, 0.6242953632895942, 0.33797360333339005, -0.190018102639817, -0.9015762184224756, -1.6894099353310925, -2.413981951587556, -2.9287502075122887, -3.10928143933081, -2.880670248497418, -2.2375973924078205, -1.2523984671351325, -0.06856533941943264, 1.1201727866838402, 2.102148084272246, 2.6859058766166237, 2.737139710766601, 2.2071201651121948, 1.1465653083033154, -0.2985624146150704, -1.909449621543977, -3.4315178122807124, -4.619604172551656, -5.282724785100695, -5.319637670530583, -4.737940032577673, -3.652510686687912, -2.263174961575608, -0.8157150905638908, 0.44611542304735197, 1.3278706767218738, 1.7212250458962421, 1.6225799936961411, 1.129462056637358, 0.4154118916292307, -0.3112619145152809, -0.8558755436734433, -1.0821999763183034, -0.9436384742490698, -0.49355711505983874, 0.12783480201120206, 0.7273582744859013, 1.1059743882343218, 1.1083894305635245, 0.6635819392856689, -0.19349552415794752, -1.324643340772471, -2.5156071380944702, -3.5220416667780072, -4.124000429081995, -4.176440748859419, -3.6438610489022314, -2.610641321820427, -1.2641970776244826, 0.14558432932516294, 1.361480551799972, 2.17589046122476, 2.476235741585728, 2.2680249517079094, 1.670042791511979, 0.8828041692370073, 0.1379120330733037, -0.3593266959263836, -0.4799448854089687, -0.2016829790098076, 0.3878073946059199, 1.1156283826459086, 1.7698364677788854, 2.1553412270022307, 2.145128522450788, 1.7135701400250765, 0.9431598520495303, 0.0029051492405246736, -0.8959576062212344, -1.5552179245341953, -1.8411965446412206, -1.7186595262795634, -1.2579138081989645, -0.6130485689057943, 0.022832667208538267, 0.4731046157614204, 0.6283569032118167, 0.4779146086414871, 0.11276636298623348, -0.3016080143188214, -0.5754628031451599, -0.5541435041185049, -0.16946028783829192, 0.5324978389802563, 1.3966311370214166, 2.1976318073833045, 2.7030954930563964, 2.744128930620949, 2.2733931796731994, 1.3927618266831168, 0.3401766598192821, -0.5639316973551074, -0.9989388784683766, -0.7345181751462061, 0.29486706822891373, 1.952928983307215, 3.9147018856078626, 5.729937297002608, 6.9234846897611675, 7.10896489746623, 6.087443844376638, 3.9055084945140677, 0.8566730549311831, -2.5759242470152595, -5.822648468489839, -8.351567047421794, -9.783375948253289, -9.968973901791802, -9.011211960984618, -7.226776033769045, -5.059561477876019, -2.969127228915656, -1.3235828360132909, -0.3240528835037442, 0.021621625642609558, -0.12767699684924677, -0.5147775615487787, -0.8724818842100909, -1.0051568254901426, -0.8404577907995291, -0.4379138540708809, 0.045381690587194344, 0.4187068156219317, 0.5293617317812711, 0.318416815188957, -0.15739526936792056, -0.744367938377551, -1.244545336289901, -1.4847928182504806, -1.3790269269628943, -0.96236420468738, -0.3848086898963803, 0.13484452382397147, 0.38105518285069834, 0.21665963111834105, -0.3637148324490969, -1.2206820286864166, -2.1039982433562487, -2.7248954204887688, -2.8456599754724814, -2.3587723917029444, -1.3299702643939868, 0.010142301996699995, 1.3257874320657406, 2.27077199513949, 2.590485034313328, 2.200016718755003, 1.2136089654857531, -0.08507389189308633, -1.324361050961179, -2.15398280402902, -2.3495089084445926, -1.8796301398186948, -0.9149401281017406, 0.22534871638908496, 1.1730243250206793, 1.6263174936174782, 1.4451593266235847, 0.6959849991096863, -0.36876590220809824, -1.3908707923280355, -2.0216137888411847, -2.0358705760868623, -1.4084110822756213, -0.32719873817319417, 0.8618891967171353, 1.7626590479931377, 2.0551656140240673, 1.6011262775103843, 0.49400618659396184, -0.9633957046345292, -2.3481855651077757, -3.2463019331844007, -3.380836341915814, -2.6989849478760863], 'positive_zeros': ['1.69144844888920009610292591648579', '2.66451574357743769318009670601817', '4.08563273524599149871051386291570', '5.66418769884118381148197147273377', '6.78660310245999746138955978208108', '7.73714846452564120208314480355846', '8.773935284643837596290484626399547', '9.270052668138818769084969980891649', '9.960610785746302660534895147946499', '11.13201731544092088686923305461442'], 'prelabel': '2-406-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.8005350099523156, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1694940677697994416, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.69144844888920009610292591649', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.66451574357743769318009670602', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.08563273524599149871051386292', 'prec': 100}}