-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3279501356215263058587036559310', 'a10': [-6.0, 0], 'a2': [0, -2.0], 'a3': [0, 0], 'a4': [-2.0, 0], 'a5': [0, -3.0], 'a6': [0, 0], 'a7': [0, 1.0], 'a8': [0, 0], 'a9': [-3.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.446302559117473, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, -1.0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [7, 13], 'central_character': '1183.337', 'coefficient_field': 'CDF', 'conductor': 1183, 'conductor_radical': 91, 'conjugate': '2131932809181663641631814113899', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.0], [-2.0, 0]], [[1.0, 0], [0, 0], [3.0, 0]], [[1.0, 0], [0, 3.0], [-5.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, -6.0], [-11.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.0, 0], [17.0, 0]], [[1.0, 0], [0, -5.0], [-19.0, 0]], [[1.0, 0], [3.0, 0], [23.0, 0]], [[1.0, 0], [5.0, 0], [29.0, 0]], [[1.0, 0], [0, 3.0], [-31.0, 0]], [[1.0, 0], [0, -4.0], [-37.0, 0]], [[1.0, 0], [0, 6.0], [-41.0, 0]], [[1.0, 0], [-1.0, 0], [43.0, 0]], [[1.0, 0], [0, 7.0], [-47.0, 0]], [[1.0, 0], [9.0, 0], [53.0, 0]], [[1.0, 0], [0, 8.0], [-59.0, 0]], [[1.0, 0], [10.0, 0], [61.0, 0]], [[1.0, 0], [0, 6.0], [-67.0, 0]], [[1.0, 0], [0, 8.0], [-71.0, 0]], [[1.0, 0], [0, -13.0], [-73.0, 0]], [[1.0, 0], [-3.0, 0], [79.0, 0]], [[1.0, 0], [0, -15.0], [-83.0, 0]], [[1.0, 0], [0, 3.0], [-89.0, 0]], [[1.0, 0], [0, -7.0], [-97.0, 0]], [[1.0, 0], [-14.0, 0], [101.0, 0]], [[1.0, 0], [-4.0, 0], [103.0, 0]], [[1.0, 0], [4.0, 0], [107.0, 0]], [[1.0, 0], [0, 2.0], [-109.0, 0]], [[1.0, 0], [3.0, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 76, 'label': '2-1183-13.12-c1-0-76', 'leading_term': '2.5185991297431027541226552983428053298325105', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/1183/2/c/b/337/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.65108655007417e-60, -0.15271628437547496, -0.31625552108327887, -0.49145432028345504, -0.6791342232185777, -0.8800325901158668, -1.094733208529494, -1.3235997293745803, -1.5667144446919674, -1.8238242813307988, -2.0942953167437723, -2.3770766950543543, -2.670674550030808, -2.9731364043369015, -3.282046468094261, -3.5945322558130033, -3.9072829359577366, -4.21657978926299, -4.518339059590964, -4.8081673243712855, -5.081429288625191, -5.333327621644697, -5.558994117402204, -5.753591080651264, -5.912421434580548, -6.031045628495943, -6.1054030121211476, -6.13193495421592, -6.107706635110848, -6.030524153119969, -5.899043370675897, -5.712866803333446, -5.472624837649247, -5.180037664130411, -4.83795453771397, -4.450367335742949, -4.02239587314535, -3.56024305289109, -3.071118668245409, -2.563131518168234, -2.0451504295930274, -1.5266357764577059, -1.0174441168853408, -0.5276096044957375, -0.0671068320115125, 0.354399302452363, 0.727810292192915, 1.0448501900918186, 1.298313661214268, 1.4822980523820348, 1.5924115727898072, 1.6259499040114367, 1.5820340575222407, 1.4617030767228902, 1.2679562318709785, 1.0057406630867578, 0.6818819605467937, 0.3049568932214334, -0.1148906409377288, -0.5661874275680862, -1.0364175365986563, -1.5123508324827801, -1.9804047400645406, -2.4270290397144345, -2.839102167246728, -3.2043265361839173, -3.5116098392365465, -3.7514191677933906, -3.9160951437624405, -4.000114101603402, -4.000287685775461, -3.915891016507974, -3.748712781339272, -3.503023168410464, -3.185458389120574, -2.804823545635244, -2.3718186732269126, -1.898695809780853, -1.398857791682014, -0.8864120236846841, -0.3756946028338909, 0.11921821341595333, 0.5849932073328543, 1.0094997662316263, 1.3822279202766552, 1.6946481115286018, 1.9404978299340983, 2.11598280663151, 2.2198836079335544, 2.2535621152800944, 2.2208663712599552, 2.127936461355622, 1.9829183111309574, 1.7955963258334717, 1.5769594992608993, 1.3387187938220775, 1.0927960822256908, 0.8508066052880684, 0.6235576336091547, 0.4205857550302074, 0.24975391972904587, 0.11692708189865521, 0.0257420503563965, -0.02251688382459816, -0.028929676817123103, 0.0031620847157045155, 0.06836845560105421, 0.1595659910784403, 0.2683000232564754, 0.38525561732501695, 0.5007746757356645, 0.6053938529314636, 0.6903763004772819, 0.7482099071299722, 0.7730456964221625, 0.7610523969892042, 0.7106668416374334, 0.6227246458852187, 0.5004613671995382, 0.3493807971611611, 0.17699388834843383, -0.007561269655040261, -0.19400138844068046, -0.3714588184691675, -0.5290932742169893, -0.656722718317762, -0.7454394880235216, -0.7881772658548637, -0.7801958190045301, -0.7194535661423453, -0.6068428881435246, -0.4462694985826084, -0.2445648586012225, -0.011229207405999043, 0.24198813212521156, 0.5016553855089206, 0.7533474273262339, 0.9824251295080074, 1.1748663709919624, 1.3181055476608994, 1.4018359636049356, 1.4187293720883036, 1.365029280069723, 1.2409794198032236, 1.0510558788983781, 0.8039804897227871, 0.5125038119532215, 0.19295789429110266, -0.13540861485557626, -0.45128816589212517, -0.7323284802937916, -0.956256800709809, -1.1020598026410324, -1.1511592946835902, -1.0885213493018064, -0.9036372577528652, -0.5913187921086227, -0.15225760838046654, 0.4066910190287821, 1.072527011153464, 1.826438811968398, 2.6444470199002845, 3.4983375003529864, 4.356846985711123, 5.1870493351049145, 5.955877985837851, 6.631710454347395, 7.185934678409542, 7.594415003690724, 7.8387779715615, 7.907444798435427, 7.796348347980179, 7.509287047353647, 7.057885925972401, 6.4611549049849115, 5.744655628384789, 4.939309389686861, 4.079898912866117, 3.203334751730964, 2.3467718186338753, 1.5456721257825636, 0.831915504907761, 0.23206039540327653, -0.2341484289466797, -0.5549389730113263, -0.727267406787836, -0.7571191072936201, -0.6593280039494974, -0.45691226926242556, -0.17995057349048435, 0.1359513456782688, 0.45153059207709184, 0.7259802702280257, 0.9191972782382889, 0.9940463362661867, 0.9185183593893905, 0.6676644245018044, 0.22519633458128208, -0.41533924513889514, -1.2498846730137558, -2.263739025400236, -3.431986560770539, -4.720472630574056, -6.08728364700951, -7.484659566282256, -8.861242732142474, -10.164547299617023, -11.343520014492274, -12.351056717635156, -13.146340040948479, -13.696872403951787, -13.980094210565813, -13.98449926746081, -13.710186700722998, -13.16881952288392, -12.382992752152468, -11.385046732902893, -10.215392152103007, -8.92044038259639, -7.550254603925432, -6.1560523476901094, -4.787697763003716, -3.4913215175568504, -2.3071978381481824, -1.267992231860794, -0.3974708554693817, 0.290265336958428, 0.7909899650198172, 1.110005521277675, 1.2612767931652322, 1.2661080549963717, 1.1514549341821838, 0.9479823055498998, 0.6879929589872256, 0.40335730702487416, 0.12357173374634517, -0.12593746373846862, -0.32516551449503495, -0.4604609884829251, -0.5249915295290767, -0.5187282582893102, -0.44796542697023434, -0.32442227591460204, -0.1640009596786901, 0.014703886916651771, 0.19203330469483204, 0.3489117984614536, 0.4683973058313918, 0.5370245513491194, 0.5458490550131988, 0.491121420556408, 0.37454862947198647, 0.20312903459830814, -0.011421499005908612, -0.25360546193152095, -0.5053687539085309, -0.747521369641245], 'positive_zeros': ['2.58707040853750830679738532681098', '3.38289976035022851334095946634223', '4.73171856981058939699108533044493', '6.00146053406771464552867517460022', '6.14853283728876422680485728492392', '7.08747754694164583198811242243948', '7.79564503359671757395302267518159', '8.647665992310408386362152389603714', '9.216434654102498881900676986568288'], 'prelabel': '2-1183-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0734837821464867, 'root_angle': -0.3128329581890012, 'root_number': '0.5547001962252291220183417334569993763463533190531148020 - 0.8320502943378436830275126001854990645195299785796722030*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1564164790945006', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.58707040853750830679738532681', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.38289976035022851334095946634', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.73171856981058939699108533044', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 9.446302559117473, 'bad_primes': [7, 13], 'central_character': '13.12', 'conductor': 1183, 'conductor_radical': 91, 'degree': 2, 'index': 76, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1183/2/c/b/337/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '2-1183-13.12-c1-0-76', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-1183-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0734837821464867, 'root_angle': -0.1564164790945006, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.58707040853750830679738532681', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3279501356215263058587036559310', 'Lhash_array': ['3279501356215263058587036559310'], 'label': '2-1183-13.12-c1-0-76', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1183/2/c/b/337/1'}