Table lfunc_lfunctions
L-functions
{'Lhash': '2676519555124293661795302287908', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, -3.8048984355764595], 'a4': [0.0, 0.0], 'a5': [-10.47205078547356, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 18.520259177452136], 'a8': [0.0, 0.0], 'a9': [66.52274789494781, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.577435865390568, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, -18.520259177452136]]]], 'bad_primes': [2, 7], 'central_character': '112.15', 'coefficient_field': 'CDF', 'conductor': 112, 'conductor_radical': 14, 'conjugate': '390243544525087628650646122199', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 3.8048984355764595], [-81.0, 0]], [[1.0, 0], [10.47205078547356, 0], [625.0, 0]], [[1.0, 0], [0, -18.520259177452136]], [[1.0, 0], [0, 224.69296014455242], [-14641.0, 0]], [[1.0, 0], [312.9483711478238, 0], [28561.0, 0]], [[1.0, 0], [321.9294501207052, 0], [83521.0, 0]], [[1.0, 0], [0, -199.4683718518018], [-130321.0, 0]], [[1.0, 0], [0, 450.504334467549], [-279841.0, 0]], [[1.0, 0], [807.3599111153418, 0], [707281.0, 0]], [[1.0, 0], [0, 141.63045868337733], [-923521.0, 0]], [[1.0, 0], [667.8093850374502, 0], [1874161.0, 0]], [[1.0, 0], [-2679.075460898236, 0], [2825761.0, 0]], [[1.0, 0], [0, 3003.840649650167], [-3418801.0, 0]], [[1.0, 0], [0, -201.11019381473278], [-4879681.0, 0]], [[1.0, 0], [-1514.8622478615728, 0], [7890481.0, 0]], [[1.0, 0], [0, -4972.944787102038], [-12117361.0, 0]], [[1.0, 0], [-5627.764751998315, 0], [13845841.0, 0]], [[1.0, 0], [0, 5773.684449197944], [-20151121.0, 0]], [[1.0, 0], [0, -3854.5026200168286], [-25411681.0, 0]], [[1.0, 0], [2627.423382783893, 0], [28398241.0, 0]], [[1.0, 0], [0, -7405.7184119820695], [-38950081.0, 0]], [[1.0, 0], [0, 7216.048702626495], [-47458321.0, 0]], [[1.0, 0], [2842.3821157881507, 0], [62742241.0, 0]], [[1.0, 0], [-2062.711232628703, 0], [88529281.0, 0]], [[1.0, 0], [6148.396882330495, 0], [104060401.0, 0]], [[1.0, 0], [0, -10583.508731391941], [-112550881.0, 0]], [[1.0, 0], [0, -2154.0589171170027], [-131079601.0, 0]], [[1.0, 0], [3861.979202361116, 0], [141158161.0, 0]], [[1.0, 0], [-223.71706512231418, 0], [163047361.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 12941139, 'index': 10, 'label': '2-112-4.3-c4-0-10', 'load_key': 'CMFs-workshop', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/112/5/d/b/15/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 27}, 'plot_values': [0.7404138548043891, 1.1360558976863004, 1.4907277054638841, 1.7877405111589093, 2.01068043959166, 2.1438853913184057, 2.173404733663261, 2.0884155185298274, 1.8829760180096278, 1.5579077228503726, 1.1225204369770518, 0.5958431653321092, 0.007008970260713831, -0.6055224971830557, -1.1961259665445831, -1.7156187061266908, -2.116167200919139, -2.3570966808366656, -2.4109595641347354, -2.2690135252606827, -1.9451469188433912, -1.4773149990438352, -0.9257474415421234, -0.36756435525801734, 0.11203070856884678, 0.43118868451218556, 0.5240731179360936, 0.35283471364548896, -0.08324379978367935, -0.7434664123841561, -1.5478183781074437, -2.3860350694471935, -3.1330416605257874, -3.668856987909282, -3.899898885040346, -3.7778873078561976, -3.3124476537365775, -2.5742060161835147, -1.6866304752009347, -0.8069241095003407, -0.09856713760529334, 0.29982761687354775, 0.303333848801991, -0.0990239112217747, -0.8376600006918986, -1.7721566588018651, -2.7166968466865264, -3.4769876005983607, -3.891434305787002, -3.8676426984336207, -3.405559182591638, -2.6008915072558447, -1.6265628365135392, -0.6950351842168325, -0.009234789694537858, 0.2867343631169112, 0.1449311007825512, -0.371157677134383, -1.0987372045667119, -1.8138841273321427, -2.287574694455736, -2.3460331126560106, -1.9197036485631256, -1.0670264623622832, 0.03501174439519713, 1.1331078853552967, 1.9631642106273803, 2.322479765931665, 2.12895364990187, 1.4499236180546167, 0.4906646129280246, -0.45661233359370546, -1.091049655123205, -1.1878643737945018, -0.6654830396910726, 0.3852433668897142, 1.720132205999327, 3.0057735673720174, 3.9117958803244304, 4.205150170642687, 3.818377816043386, 2.870410209378529, 1.6320141160431363, 0.4447425771163516, -0.38290233188702627, -0.6702710210706313, -0.42011825221959986, 0.1839178059346736, 0.8386912111589209, 1.2233872176125453, 1.1093800146629262, 0.441684433429354, -0.636431461045331, -1.8261543220538368, -2.7712373558910177, -3.1801295605188264, -2.9310254672105156, -2.1226793035501483, -1.050823031846547, -0.11490120140936037, 0.315658393287186, 0.030891460009763595, -0.9398816809351099, -2.327858074375274, -3.7074916296961034, -4.636380487788405, -4.8052680084503985, -4.145746506843225, -2.8564376432385474, -1.3362576603850496, -0.04640060429190736, 0.6509449092241053, 0.6193515237057398, -0.006297576455975481, -0.8734210834131899, -1.5461528475802502, -1.6716065325626348, -1.115924516986366, -0.018018718993497333, 1.260971667298505, 2.2750234760489256, 2.665956413389631, 2.305059672025556, 1.347496910562042, 0.1760423902669348, -0.7463331940702901, -1.0588412491812491, -0.6484517862763483, 0.3005819270408175, 1.375820922692743, 2.099892756814413, 2.124598498660979, 1.3779773575404306, 0.10293877924300913, -1.2318256646209587, -2.116435860548652, -2.2075267737989597, -1.4747330428319736, -0.2239172692010957, 1.016297645934168, 1.7023562355160209, 1.4955183955777291, 0.4038440072209452, -1.213549207766607, -2.784459568279969, -3.749537375069608, -3.784394145007725, -2.926218634652316, -1.5519313452047163, -0.21672184897579116, 0.5790593400939812, 0.5956314177979756, -0.05585947581249374, -0.9770830629370901, -1.6721715164078517, -1.7793826221610158, -1.2412013547589207, -0.3352025341306159, 0.4508473308801698, 0.6461045270177175, 0.024603069846291344, -1.2707481791130801, -2.7690069036209755, -3.86481635594005, -4.082832044912786, -3.2958963012823066, -1.7967224944915094, -0.18568368785940328, 0.8808863521575705, 0.9732640258882478, 0.07631960360071528, -1.4029456590564082, -2.814586655809676, -3.553615221879179, -3.328061489805299, -2.2858331947126116, -0.9419277688804434, 0.06163222731868245, 0.2535038115449902, -0.44886295948728144, -1.702094880613274, -2.8985049676638783, -3.451201695115241, -3.068771573813644, -1.8895762658703106, -0.4114960564693018, 0.7497724295943404, 1.1580530764812262, 0.7657739292612062, -0.0679427273436385, -0.7611238279928428, -0.8068100352365468, -0.039216053610410063, 1.2650620226183003, 2.5056899832543693, 3.044619883020703, 2.522761936527693, 1.0515742869397322, -0.818756228930011, -2.345370306138068, -2.9380726620036577, -2.437306733158555, -1.18752428135514, 0.13335297576444882, 0.8481304929757968, 0.6156568540180046, -0.39855368428067467, -1.6031327639916404, -2.2761750165384846, -1.9307682157998698, -0.569407185819668, 1.300952307015842, 2.9034109194509528, 3.560838268224561, 3.0179878146994787, 1.556276120608009, -0.15460795404742864, -1.3913346540966764, -1.7267501851399405, -1.2169604159454621, -0.33251562653931593, 0.3260725456029978, 0.3750905827829325, -0.13022974790414837, -0.7201542812115926, -0.7727382818701692, 0.12336567394639687, 1.9010899988856693, 3.9927787510643897, 5.577639882323301, 5.979473298220255, 5.011063012185508, 3.082826187048103, 1.0116438140805892, -0.37883424941956323, -0.6639807835450627, -0.020542143239380847, 0.881055226185595, 1.2403047149273034, 0.5574173851217363, -1.0941342406422991, -3.0968372837321527, -4.6050577326773485, -4.9809519558822934, -4.119950196226327, -2.4944311004402526, -0.8952019837279026, -0.0126002048280885, -0.08476490957964608, -0.8028440763071258, -1.521386739455457, -1.6536897598381823, -1.0289044124857623, -0.007826845291914492, 0.712166914943135, 0.4983080388804234, -0.8334849815442588], 'positive_zeros': ['2.11140163909709010462742278551376', '4.17318593673444129606008345074069', '4.89480965811893447690303321702533', '7.06311605295124262215761613841206', '7.52737935553255687289016754070695', '9.495407235836734815232667144893895', '9.905407909119638717354661552253618', '11.24462787423654551284789224535679', '12.39182917145638971239852698821151', '13.12674702844154079651406853395229'], 'prelabel': '2-112-4.3-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4025631317273994, 'root_angle': 0.4166666666666667, 'root_number': '-0.8660254037844387 + 0.49999999999999994*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.416666666667', 'prec': 40}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.11140163909709010462742278551', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '4.17318593673444129606008345074', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.89480965811893447690303321703', 'prec': 100}}