Table lfunc_lfunctions
L-functions
{'Lhash': '1983656412225350356424228541828', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.193527085331054, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.8378527913529716, 0.0], 'a8': [0.0, 0.0], 'a9': [-1.575493096581159, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 38.647594578299724, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5, 11], 'central_character': '4840.1', 'coefficient_field': 'CDF', 'conductor': 4840, 'conductor_radical': 110, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.193527085331054, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.8378527913529716, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.255461807853298, 0], [13.0, 0]], [[1.0, 0], [-6.448988893184352, 0], [17.0, 0]], [[1.0, 0], [-1.2511986792871026, 0], [19.0, 0]], [[1.0, 0], [4.355674293978082, 0], [23.0, 0]], [[1.0, 0], [0.7264792897434773, 0], [29.0, 0]], [[1.0, 0], [11.079008928264765, 0], [31.0, 0]], [[1.0, 0], [11.508603991095608, 0], [37.0, 0]], [[1.0, 0], [-7.924269503640726, 0], [41.0, 0]], [[1.0, 0], [-0.6068729732651847, 0], [43.0, 0]], [[1.0, 0], [3.981941097596775, 0], [47.0, 0]], [[1.0, 0], [-6.8328984083896644, 0], [53.0, 0]], [[1.0, 0], [1.4120109599838475, 0], [59.0, 0]], [[1.0, 0], [9.752079752618387, 0], [61.0, 0]], [[1.0, 0], [-12.58993254397136, 0], [67.0, 0]], [[1.0, 0], [6.796646827134519, 0], [71.0, 0]], [[1.0, 0], [10.065213154427735, 0], [73.0, 0]], [[1.0, 0], [-6.519765006580318, 0], [79.0, 0]], [[1.0, 0], [-0.6443257060219177, 0], [83.0, 0]], [[1.0, 0], [-9.397230489486113, 0], [89.0, 0]], [[1.0, 0], [4.661909808868914, 0], [97.0, 0]], [[1.0, 0], [-10.10775404659647, 0], [101.0, 0]], [[1.0, 0], [3.7113485879561643, 0], [103.0, 0]], [[1.0, 0], [7.692779788448464, 0], [107.0, 0]], [[1.0, 0], [3.0656879539839634, 0], [109.0, 0]], [[1.0, 0], [10.516836805964406, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 19956193, 'index': 94, 'label': '2-4840-1.1-c1-0-94', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/4840/2/a/y/1/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 17}, 'plot_values': [-1.1607382012416778e-60, 0.21301446170797336, 0.42533199385915754, 0.6362138704977395, 0.8448403640737727, 1.050276539905133, 1.251445117420567, 1.4471080083401175, 1.6358576219450696, 1.8161184967166495, 1.9861593191920228, 2.1441149543467466, 2.2880177516020086, 2.4158371081117855, 2.5255260586185346, 2.6150735064127955, 2.6825605993704835, 2.7262196770117297, 2.7444941606375104, 2.736097724204683, 2.700071067512748, 2.6358346170763, 2.5432355072051323, 2.4225872487584734, 2.274700580421081, 2.1009041213359625, 1.9030536077005908, 1.683528701296946, 1.445216605048323, 1.1914820079424617, 0.9261232055158394, 0.6533145971619917, 0.3775361406004758, 0.10349073803960399, -0.16398907247598646, -0.4200433549055255, -0.659893803790084, -0.8789570846478376, -1.072959712325323, -1.2380514569074845, -1.3709141007653467, -1.468862285670074, -1.5299331947696337, -1.5529619175808218, -1.5376395513775745, -1.4845514008867093, -1.3951930482209545, -1.27196257122431, -1.1181277820633115, -0.9377680266169277, -0.735690813240351, -0.5173243079058196, -0.2885875199122872, -0.05574078443552833, 0.1747801002934967, 0.3965420287349179, 0.6033003727598373, 0.7891872284489424, 0.9488965872659383, 1.0778606760289182, 1.17241166227677, 1.2299230564137162, 1.2489254666743221, 1.2291918788152376, 1.1717883344493119, 1.0790867583757409, 0.9547377177037041, 0.8036020590752088, 0.6316416338401319, 0.4457706481960886, 0.2536705251743085, 0.06357249369907536, -0.11598661943886478, -0.2764287726568837, -0.4094116594068428, -0.5071098328117457, -0.5624910702603081, -0.5695787728552768, -0.5236912212213435, -0.42164884779210504, -0.26194134130227154, -0.04484736586248268, 0.2274990626288486, 0.5510999746054412, 0.9201453007283984, 1.3271259368886144, 1.7630067333783128, 2.217456028909385, 2.679126279193528, 3.1359783547481253, 3.575640278311407, 3.9857896112220113, 4.354547447632, 4.670871094803046, 4.9249320557125085, 5.108465922533371, 5.215081257039265, 5.240515480892795, 5.182827211853999, 5.042516330049818, 4.822565292817543, 4.528397771886385, 4.167753482442072, 3.7504810169555998, 3.2882534848928446, 2.794214683686295, 2.282566275440642, 1.768108908389958, 1.265752298884531, 0.7900108858138772, 0.3545027064791974, -0.028530439233653643, -0.348663709921901, -0.5976739163644659, -0.7698528524187624, -0.8622361320177314, -0.874737170768344, -0.8101791992616211, -0.6742218146031852, -0.47518244006251825, -0.22375702901737962, 0.0673517318234192, 0.38388674758882463, 0.7105540321866068, 1.0315872121982366, 1.3313385691842794, 1.5948746606053372, 1.8085538632612002, 1.9605633544521806, 2.0413941045584156, 2.0442343849226674, 1.9652650455957374, 1.8038433025380531, 1.5625658745273932, 1.247206878685399, 0.8665307587971918, 0.4319854935328095, -0.042713786918438176, -0.5420960589618707, -1.049521721918499, -1.5478237261153847, -2.019977664953713, -2.4497743392408227, -2.8224677082235465, -3.12537164930434, -3.348380563873008, -3.4843915500719005, -3.5296095284292526, -3.48372122297391, -3.3499290987829196, -3.1348420333752385, -2.848225424539545, -2.5026193649265727, -2.1128391913334656, -1.6953778955593068, -1.2677343306708264, -0.8476946539127932, -0.4525968433478173, -0.09860928177679448, 0.19994575826273475, 0.43119439162766227, 0.5862126200503661, 0.6594045157583094, 0.6487396061461664, 0.5558378837955, 0.38589738182489747, 0.14746610175810593, -0.1479330382353805, -0.4863089591853867, -0.8518195722008522, -1.2274728381762263, -1.5958811791509575, -1.9400359246755994, -2.2440671788108286, -2.493954744338634, -2.6781575584290587, -2.788132424952399, -2.8187175486492624, -2.7683622944719346, -2.6391914610048093, -2.436899869965505, -2.170480897744713, -1.8518003513099701, -1.495034455562246, -1.115997319769945, -0.731388762646703, -0.35799751886419784, -0.011897402733216577, 0.29232518364851623, 0.5422750120388703, 0.7283484754824943, 0.8442006404159006, 0.8870548438794772, 0.8578380572793648, 0.7611334532962679, 0.6049503844546684, 0.4003208980323406, 0.16074054383654124, -0.09852084538193719, -0.36120590579011164, -0.6109161785215642, -0.8319767822626267, -1.01027624076266, -1.1340388362309808, -1.1944894203144423, -1.1863752020821425, -1.1083154647608753, -0.9629581627134145, -0.7569315567963283, -0.500589031612231, -0.20755552598693205, 0.10590590380826514, 0.42167948362710517, 0.7206979779426587, 0.983917112113127, 1.1933158623988807, 1.3328729595837319, 1.3894700133572113, 1.353674193610006, 1.2203583300736909, 0.9891234209354285, 0.6644975676482546, 0.25589586911568735, -0.22266267768319573, -0.7530732639000158, -1.3138785162617241, -1.8811859944252547, -2.429729242774518, -2.9340237341324773, -3.3695633282611084, -3.713999737459133, -3.9482471538279005, -4.057456720655822, -4.0318108540796445, -3.867095328833247, -3.5650171872503855, -3.1332484478917055, -2.5851887149130777, -1.9394534854720118, -1.2191085430535085, -0.45068362527586653, 0.33699009136573066, 1.114064835653741, 1.8510227933849386, 2.520019904653545, 3.096161769957567, 3.558649102178059, 3.891735901894099, 4.0854521957527234, 4.136054363670007, 4.046179257064051, 3.824692833507288, 3.486239180767226, 3.0505108101395093, 2.541275196512106, 1.985204998126986, 1.4105695447328463], 'positive_zeros': ['1.56482899299555443109336624908352', '2.49561686725426978994739439666127', '3.34429622718569908729876339984895', '3.80527778884990097102940261142842', '5.19936486244070317479880685097552', '5.66146745069945851023919856595693', '6.41777743316307942878589698341397', '7.42070894767394719178986604651799', '7.80564621191749223666525872411080'], 'prelabel': '2-4840-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.216718956032975, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.56482899299555443109336624908', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.49561686725426978994739439666', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.34429622718569908729876339985', 'prec': 100}}