Table lfunc_lfunctions
L-functions
{'Lhash': '2289833943864756533257648022440', 'a10': [-0.19009799585123366, 0.3588725890547541], 'a2': [1.2497112848549035, 0.6619831602890713], 'a3': [-1.5997207054091265, -0.6639982414775861], 'a4': [1.1235565909873872, 1.6545756515943297], 'a5': [0.0, 0.2871643982125205], 'a6': [-1.5596333638461135, -1.8887942636449468], 'a7': [0.0, -4.183905926262579], 'a8': [0.308820132150279, 2.811517406309035], 'a9': [2.1182126706293465, 2.124423470493887], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.090715699489701, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [-1.2497112848549035, -0.6619831602890713]]], [3, [[1.0, 0], [1.5997207054091265, 0.6639982414775861]]], [37, [[1.0, 0], [-5.227510780194855, 3.110165758114281]]]], 'bad_primes': [2, 3, 37], 'central_character': '888.443', 'coefficient_field': 'CDF', 'conductor': 888, 'conductor_radical': 222, 'conjugate': '713652592370215228246625825875', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.2497112848549035, -0.6619831602890713]], [[1.0, 0], [1.5997207054091265, 0.6639982414775861]], [[1.0, 0], [0, -0.2871643982125205], [-5.0, 0]], [[1.0, 0], [0, 4.183905926262579], [-7.0, 0]], [[1.0, 0], [0, 4.656157729865138], [-11.0, 0]], [[1.0, 0], [5.633718366042966, 0], [13.0, 0]], [[1.0, 0], [1.6826042898677407, 0], [17.0, 0]], [[1.0, 0], [0, 5.898701509557097], [-19.0, 0]], [[1.0, 0], [0, -2.8553714308807034], [-23.0, 0]], [[1.0, 0], [0, 4.390312779648217], [-29.0, 0]], [[1.0, 0], [4.814769613288789, 0], [31.0, 0]], [[1.0, 0], [-5.227510780194855, 3.110165758114281]], [[1.0, 0], [0, 10.709657972941924], [-41.0, 0]], [[1.0, 0], [0, -2.3252404820544177], [-43.0, 0]], [[1.0, 0], [-9.32438162493229, 0], [47.0, 0]], [[1.0, 0], [1.1698400970007683, 0], [53.0, 0]], [[1.0, 0], [-14.917637530078471, 0], [59.0, 0]], [[1.0, 0], [10.062779111486336, 0], [61.0, 0]], [[1.0, 0], [9.330203001632258, 0], [67.0, 0]], [[1.0, 0], [-3.7250466225307712, 0], [71.0, 0]], [[1.0, 0], [0.9250821423362328, 0], [73.0, 0]], [[1.0, 0], [2.8956486000241406, 0], [79.0, 0]], [[1.0, 0], [0, 0.7722302912233507], [-83.0, 0]], [[1.0, 0], [-8.300295094336718, 0], [89.0, 0]], [[1.0, 0], [0, -15.355175758003242], [-97.0, 0]], [[1.0, 0], [5.888656716412326, 0], [101.0, 0]], [[1.0, 0], [3.915653417154059, 0], [103.0, 0]], [[1.0, 0], [0, -7.537999870056771], [-107.0, 0]], [[1.0, 0], [-5.803588838851007, 0], [109.0, 0]], [[1.0, 0], [-14.173990656589302, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 16462833, 'index': 115, 'label': '2-888-888.443-c1-0-115', '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/888/2/c/d/443/79', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [1.4566452179370029, 1.6975325930864815, 1.9199500418559363, 2.121521260623611, 2.2944861855401286, 2.426703631365803, 2.5034254131423377, 2.5094950317174076, 2.431705767134711, 2.2611198966089896, 1.995165731362093, 1.6393098598063132, 1.2080810887281523, 0.7252263650573753, 0.22282228137202678, -0.26074695586485097, -0.6839074581153546, -1.0059180163740646, -1.1914438720698857, -1.215184207649404, -1.0659549087986693, -0.7495968686560994, -0.29013779493514624, 0.2712090877802367, 0.8793786785461232, 1.4709723993900456, 1.981466239855854, 2.3532866287248235, 2.5436842092888803, 2.5312210354812428, 2.3197474044030417, 1.9389989131593817, 1.4413797918586484, 0.8950681460629019, 0.37420351845602084, -0.052504762325702115, -0.33298854969280395, -0.44092513379207, -0.38096481193856163, -0.18880722164174676, 0.07435730435050658, 0.33254535973821, 0.5093106669462093, 0.5433468041919925, 0.4024898026544943, 0.09322096195940952, -0.3367009523974907, -0.8037934113005835, -1.2024597687086018, -1.4249231059495107, -1.3842901057310213, -1.0365354663102062, -0.39688790997879425, 0.45335423449725964, 1.3721494838335782, 2.174675221104939, 2.661997993201829, 2.6562063305793737, 2.0360213057370404, 0.7661546021183344, -1.0858101139175278, -3.3494492676013117, -5.770042508584377, -8.043803473017702, -9.864608510647374, -10.974409143201877, -11.20822816144606, -10.525064256892588, -9.018213110286098, -6.902136894445728, -4.477434318802266, -2.0798183457371366, -0.022389645954808475, 1.457862003322408, 2.2389280860431358, 2.330327605200412, 1.8640347399366777, 1.0617193231807012, 0.18518315325363668, -0.5195388519578173, -0.8725590839534896, -0.7943381159675782, -0.3166191576545042, 0.43178388701592796, 1.260540141214812, 1.966037495904915, 2.38077046352549, 2.4121852629136655, 2.0619194050418916, 1.4212172210551905, 0.6442127460975622, -0.09369864832545648, -0.6414240176790584, -0.9097078512769554, -0.8907686768891504, -0.6548779452217679, -0.3248848887525375, -0.03572055649719397, 0.10980108437417577, 0.07623851435439927, -0.08871442156670467, -0.2634161301052923, -0.28505307751210296, 0.002114056264548089, 0.6959774600159061, 1.7976923663689643, 3.196607673219843, 4.685019916703136, 6.000816960007208, 6.888233101773439, 7.161367590791683, 6.753494108742889, 5.738172926002659, 4.3151842604105966, 2.763589419972967, 1.373322185159816, 0.3730657266864471, -0.12613365241436747, -0.1557265904129459, 0.1245515206828105, 0.47680052439902887, 0.6575632314994782, 0.4926399594370329, -0.06752003058448447, -0.9286738009142325, -1.8768424162312343, -2.640204694622549, -2.972132144140921, -2.7316688556022393, -1.9373324221529333, -0.7767071509031067, 0.43365337964967093, 1.3292409208746094, 1.598330851043472, 1.0743794161918239, -0.20703337448823103, -2.0049557229914283, -3.927169240981685, -5.528997986449705, -6.4308075372426154, -6.42177249635305, -5.520188053815138, -3.971974584551502, -2.186086792879788, -0.623524055990444, 0.32966108440598507, 0.4696692626474726, -0.16820709580196014, -1.3200602525171596, -2.5688997140036367, -3.4641918760411126, -3.651409860474714, -2.974405126400482, -1.5210690899846557, 0.40086411922565973, 2.3506770485861823, 3.87870269444773, 4.651278910997649, 4.540382499647083, 3.6525086263024775, 2.289695241894879, 0.8558762247325452, -0.2622059243101636, -0.8033694137523238, -0.6977276957482293, -0.07184566482522446, 0.8054040664537426, 1.6166509067367612, 2.098179460990421, 2.117706285520519, 1.7042314964743246, 1.0229938526850098, 0.3069735310810363, -0.22949879705456322, -0.46432599775875416, -0.4031850150025124, -0.16588720494636935, 0.06977100060622991, 0.14470839582128975, -0.013524227419266382, -0.35773144642793697, -0.7363020406136166, -0.9521001138120839, -0.8437595688540249, -0.3587814824676095, 0.41051239631229586, 1.2446421329314175, 1.865511202594961, 2.0338435232722087, 1.6412707992871611, 0.7623996472248858, -0.3555643757692373, -1.3668171983846744, -1.9426452414598614, -1.8900789090992363, -1.2307589548903852, -0.2082731999664689, 0.7846546985074336, 1.3398871445631666, 1.1861826177133807, 0.3078626249508492, -1.0148172241601352, -2.2646929569282506, -2.8348167413746275, -2.221704875057547, -0.20432156037200136, 3.050842007032131, 6.997609006776581, 10.835365798322764, 13.71867703561584, 14.990019687707031, 14.365118013977174, 12.013599378094174, 8.50959568963698, 4.6673500206535214, 1.3127105460357937, -0.9391578610049431, -1.8328310288856144, -1.5063251412370409, -0.4053438758591267, 0.8876534568651007, 1.8494041909636467, 2.1716865399752825, 1.829031454656256, 1.0429904256806124, 0.1642001867808332, -0.47900950897808175, -0.7076997664491766, -0.5494680374703733, -0.2083303471124798, 0.03626632054839964, -0.041661078176289966, -0.5104583964913622, -1.2434055928826238, -1.963409824554012, -2.352749484795198, -2.1849522898582414, -1.4265571609573142, -0.2673559757280441, 0.9352633788861594, 1.779255186548768, 1.963142685877952, 1.3989907693603976, 0.24975393319398975, -1.1244554382515703, -2.29241257799575, -2.903842901091747, -2.810974612069203, -2.1142479109634063, -1.115422927283127, -0.19651307121003292, 0.32869094156282797, 0.3332345874303059, -0.07996254267623885, -0.6269961034439235, -0.9642172446308936, -0.8337010890945556], 'positive_zeros': ['1.80636047776295137045689937889755', '2.81671023819199920359330656674170', '4.35729767016126533041626771852398', '4.96602591083851232824067193548897', '5.65451435588228534387262817333146', '6.56110977704680929520964655867879', '7.43103673891095334045606559922101', '9.001558249097744487468693887870478', '9.778746270508648494563973699838001', '10.30672896856960579132608268341554'], 'prelabel': '2-888-888.443-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6628397810401023, 'root_angle': 0.20978509551948912, 'root_number': '0.24999752305156167 + 0.9682464760938115*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.209785095519', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.80636047776295137045689937890', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.81671023819199920359330656674', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.35729767016126533041626771852', 'prec': 100}}